Question 1

In the following question, a statement about rock shows at tourist places is given, followed by two arguments I and II. You must assume the statement to be true and then decide which argument or arguments are strong. Statement: Should rock shows be …

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Introduction / Context: This is a statement and argument question about whether rock shows should be allowed to run till midnight at tourist places. Your task is to judge the strength of two arguments, one in favour and one against the idea. A strong argument is relevant, logical, and touches significant consequences of the decision. Given Data / Assumptions: We consider the following. Statement: Should rock shows be allowed to run till midnight at tourist places? Argument I: Yes, more tourists arrive due to rock shows. Tourism is good for the local economy. Argument II: No, local traditions are harmed due to tourism. Concept / Approach: An argument is strong if it gives a clear, reasonable, and significant reason related to the statement. It should not be trivial or completely unrelated. We examine whether each argument directly addresses the policy question and whether it deals with meaningful effects on society. Step-by-Step Solution: Step 1: Argument I supports the statement. It says rock shows attract more tourists, and that tourism benefits the local economy. This is a logical chain: rock shows lead to more visitors, visitors spend money, and that supports local businesses and employment. Step 2: The effect on the local economy is an important factor when deciding tourism policies. Therefore, argument I is relevant and strong. Step 3: Argument II opposes the statement. It says local traditions are harmed due to tourism. This relates directly to the potential negative cultural impact of allowing such shows till midnight. Step 4: Preservation of local traditions and culture is also a significant consideration in policy making. Therefore, argument II is also relevant and serious enough to be considered a strong argument against the proposal. Verification / Alternative check: Notice that the two arguments present two sides of a real policy debate. Argument I focuses on economic benefit, while argument II focuses on cultural harm. Both deal with substantial consequences that a decision maker would weigh. Neither argument is trivial, personal, or entirely emotional without reasoning. Why Other Options Are Wrong: Option A says only argument I is strong, ignoring the serious concern about cultural harm in argument II. Option B says only argument II is strong and overlooks the clear economic logic in argument I. Option D claims neither argument is strong, which is inconsistent with the practical relevance of both economic and cultural impacts. Common Pitfalls: Some test takers think that only arguments with statistics or very detailed reasoning are strong. In exam questions, however, an argument can be strong even if it is concise, as long as it is directly relevant and based on a reasonable cause and effect link. Final Answer: Both arguments present important and relevant reasons, so the correct choice is “Both arguments I and II are strong.”

Question 2

In the following question, two statements are given, followed by two conclusions I and II. You have to consider the statements to be true, even if they seem to be at variance with commonly known facts, and then decide which conclusion or conclusions…

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Introduction / Context: This question deliberately uses apparently contradictory ideas about bikes and two-wheelers. In real life, bikes are actually two-wheelers, but the exam asks you to ignore real world knowledge and work only with the given logical statements. Given Data / Assumptions: Treat the following as true. Statement I: No bikes are two-wheelers. Statement II: All wheels are bikes. Conclusion I: No two-wheelers are wheels. Conclusion II: All wheels are two-wheelers. Concept / Approach: “No bikes are two-wheelers” means the sets Bikes and Two-wheelers are completely disjoint. “All wheels are bikes” means the set Wheels is fully contained within the Bikes set. We must combine these relations and see how Wheels and Two-wheelers relate. Step-by-Step Solution: Step 1: From statement I, no bike can be a two-wheeler. So the intersection of Bikes and Two-wheelers is empty. Step 2: From statement II, every wheel is a bike. So the Wheels set is fully inside the Bikes set. Step 3: Since no bike is a two-wheeler, anything that is a wheel (and therefore a bike) also cannot be a two-wheeler. Hence, Wheels and Two-wheelers have no common elements. Step 4: If no element is both a two-wheeler and a wheel, then “No two-wheelers are wheels” is true. That matches conclusion I. Step 5: Conclusion II claims “All wheels are two-wheelers.” This would require the Wheels set to lie inside the Two-wheelers set. This contradicts the disjointness we just established, so conclusion II cannot be true. Verification / Alternative check: Draw a Bikes set and place the Wheels set completely inside it. Draw a separate Two-wheelers set with no overlap with Bikes. Since Wheels are inside Bikes and Bikes do not meet Two-wheelers, no wheel can be a two-wheeler. This confirms conclusion I and clearly rejects conclusion II. Why Other Options Are Wrong: Option B says only conclusion II follows, which goes directly against the combined effect of the statements. Option C says both follow, but two statements that contradict each other about the same sets cannot both be logically valid together. Option D says neither follows, ignoring the clear deduction that two-wheelers and wheels must be disjoint. Common Pitfalls: Many test takers find this question uncomfortable because the statements contradict everyday knowledge. The key rule in such reasoning problems is to suspend real world understanding and treat the given statements as a self contained logical world. Final Answer: Only conclusion I is logically valid. Therefore, the correct option is “Only conclusion I follows.”

Question 3

Consider the given statements to be true and decide which of the given conclusions or assumptions can definitely be drawn from them. Statements: 1. All books are novels. 2. Some novels are poems. Conclusions: I. Some books are poems. II. Some poems …

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Introduction / Context: This question involves three sets: books, novels, and poems. Two statements define relations between these sets. Your job is to check which of the given conclusions is forced by these relations and which is not. Given Data / Assumptions: Accept the following as true. Statement 1: All books are novels. Statement 2: Some novels are poems. Conclusion I: Some books are poems. Conclusion II: Some poems are novels. “Some” means at least one. Concept / Approach: From “All books are novels” we know the Book set lies inside the Novel set. From “Some novels are poems” we know there is at least one element in the intersection of Novels and Poems. The key question is whether that element must necessarily be a book or not, and what we can surely say about poems and novels. Step-by-Step Solution: Step 1: Statement 1 places every book inside the Novel set; there may be novels that are not books. Step 2: Statement 2 says there exists at least one element that is both a novel and a poem. Step 3: Conclusion II says “Some poems are novels.” This is exactly restating statement 2 in another form, because if some novels are poems, then some poems are necessarily novels as well. Step 4: Conclusion I claims “Some books are poems.” For this to be forced, we would need to know that the novels that are poems come specifically from the Book subset of the Novel set. However, the statements allow the possibility that the novels which are poems are not books at all. Step 5: Because it is possible to draw a consistent diagram where no book is a poem but some novels are poems, conclusion I is not necessary. Verification / Alternative check: Draw Novels as a large set. Inside it, place a smaller subset called Books. Then mark a region of Novels that overlaps with Poems. That overlapping region can be drawn outside the Books subset, showing that some novels are poems while possibly no book is a poem. In this picture, conclusion II remains true but conclusion I fails. This shows only conclusion II is guaranteed. Why Other Options Are Wrong: Option A says only conclusion I follows, which is invalid as conclusion I is not forced. Option C says neither follows, ignoring that conclusion II is a direct restatement of statement 2. Option D says both follow, which overstates what can be deduced from the given information. Common Pitfalls: Many students assume that any attribute shared by novels will automatically apply to books because all books are novels. However, you must remember that books are only a subset of novels. Other novels may have properties that books do not share, so you cannot push every property back into the subset. Final Answer: The only conclusion that necessarily follows is conclusion II. Hence, the correct answer is “Only conclusion II follows.”

Question 4

Which of the following mathematical statements is or are true? I. 2√3 > 3√2 II. 4√2 > 2√8. Compare the values of each expression carefully and then choose the correct option indicating which statement or statements are true.

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Introduction / Context: This question tests your ability to compare surds, that is, expressions containing square roots. You must evaluate the relative sizes of 2√3 and 3√2, and of 4√2 and 2√8, and then decide which of the two given statements are true. Given Data / Assumptions: We are given the following statements. Statement I: 2√3 > 3√2. Statement II: 4√2 > 2√8. All numbers are real and positive. Concept / Approach: To compare expressions involving square roots, a common technique is to square both sides, provided all values are positive. Squaring preserves the inequality direction when both sides are non negative. We can also simplify radicals, such as rewriting √8 as 2√2, to make comparisons simpler. Step-by-Step Solution: Step 1: Compare 2√3 and 3√2. Since both are positive, square each. Step 2: (2√3)^2 = 4 × 3 = 12. (3√2)^2 = 9 × 2 = 18. So 12 is less than 18, which means 2√3 is less than 3√2. Therefore, statement I is false. Step 3: Now compare 4√2 and 2√8. First, simplify √8. Since 8 = 4 × 2, √8 = √(4 × 2) = 2√2. Step 4: Substitute this into the second expression: 2√8 = 2 × 2√2 = 4√2. Step 5: Therefore, 4√2 is exactly equal to 2√8, not greater than it. So statement II is also false. Verification / Alternative check: We can approximate numerically to cross check. √2 is about 1.414 and √3 is about 1.732. Then 2√3 is roughly 2 × 1.732 ≈ 3.464, and 3√2 is roughly 3 × 1.414 ≈ 4.242, confirming that 2√3 is less than 3√2. For the second comparison, since we have already simplified 2√8 to 4√2 exactly, equality is clear. Why Other Options Are Wrong: Option A says only statement I is true, but we found statement I is false. Option B says only statement II is true, but statement II is also false. Option D says both statements are true, which again is incorrect because both fail. Common Pitfalls: Students sometimes miscompare surds by comparing the numbers under the root directly or by relying on rough mental guesses. The safe approach is to square the expressions or simplify them to a common standard form before comparison. Another common mistake is ignoring equality; in statement II many may assume that if two surds look different, one must be greater, but here they are equal. Final Answer: Both statements I and II are false. Thus, the correct option is “Neither statement I nor statement II is true.”

Question 5

Consider the given statements to be true and decide which of the given conclusions or assumptions can definitely be drawn from them. Statement 1: All animals are four-footed. Statement 2: Dog has two legs. Conclusions: I. Dog is not an animal. II. D…

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Introduction / Context: This question intentionally presents information that conflicts with real world knowledge about dogs. However, logical reasoning problems require you to accept the given statements as true inside the problem world and then derive conclusions that are consistent with them. Given Data / Assumptions: Accept the following as true. Statement 1: All animals are four-footed. Statement 2: Dog has two legs. Conclusion I: Dog is not an animal. Conclusion II: Dog is an animal. Concept / Approach: “All animals are four-footed” means every animal must have four feet. Statement 2 says that this particular dog has only two legs. We must see whether the dog can still belong to the set Animals if these statements are to remain consistent. Step-by-Step Solution: Step 1: From statement 1, any creature that is an animal must have four feet. Having four feet is a necessary condition for membership in the Animal set. Step 2: Statement 2 tells us that Dog has two legs, not four feet. For logical purposes, we treat this as meaning the dog does not satisfy the “four-footed” condition. Step 3: If being an animal requires having four feet, and this particular dog has only two legs, then the dog cannot be an animal without violating the first statement. Step 4: Therefore, to keep both statements true simultaneously, Dog must not belong to the set Animals. This makes conclusion I logically valid. Step 5: Conclusion II says “Dog is an animal.” If we accept this, then Dog, as an animal, must be four-footed, which would contradict statement 2 that Dog has two legs. So conclusion II cannot be true if the statements are accepted. Verification / Alternative check: Visualise a set called Animals that contains only four-footed creatures. If Dog had four feet, Dog could be inside this set. But the second statement tells us Dog has only two legs, forcing Dog to remain outside the Animal set to preserve the truth of statement 1. Hence, the only consistent way to interpret the information is to treat Dog as not an animal. Why Other Options Are Wrong: Option B says only conclusion II follows, but conclusion II directly conflicts with the necessary condition stated in statement 1. Option C says neither follows, but we saw that conclusion I is required for consistency. Option D says both follow, which would force a contradiction between the two statements and the conclusions. Common Pitfalls: Candidates often rely on real life knowledge that dogs are animals, which leads them to reject conclusion I. Logical reasoning questions deliberately challenge this by redefining the categories inside the question. You must temporarily abandon everyday facts and stick only to the conditions defined by the statements. Final Answer: The only conclusion that keeps the statements consistent is that Dog is not an animal. Therefore, the correct answer is “Only conclusion I follows.”

Question 6

Consider the following logical reasoning problem about relationships between astronomers, scientists, and shopkeepers. Treat the given statements as true, even if they appear to contradict common knowledge, and then decide which of the listed conclu…

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Introduction / Context: This question tests basic syllogism or statement and conclusion reasoning. We are given two categorical statements about astronomers, scientists, and shopkeepers, and then several possible conclusions. Our task is to assume that both statements are absolutely true and then check, using pure logic, which conclusions must follow in every possible situation that satisfies the statements. Given Data / Assumptions: - Statement 1: All astronomers are scientists. - Statement 2: Some scientists are shopkeepers. - We treat the word some as meaning at least one. - No extra facts beyond these statements are to be assumed. Concept / Approach: In syllogism questions, the safest method is to visualise or draw simple Venn diagrams and then see what must be true. The structure All A are B means the A circle lies completely inside the B circle. The structure Some B are C means that there is at least one overlapping region common to sets B and C. A conclusion is valid only if it holds in every possible diagram that respects the given statements. If we can imagine even one valid diagram where the conclusion fails, then that conclusion does not logically follow. Step-by-Step Solution: Step 1: Represent astronomers (A) and scientists (S) so that all astronomers are inside the set of scientists. This captures Statement 1. Step 2: Represent shopkeepers (K) such that there is at least one common region between scientists and shopkeepers, because some scientists are shopkeepers as given in Statement 2. Step 3: Check Conclusion I: All astronomers are shopkeepers. We only know that all astronomers are scientists and that some scientists are shopkeepers. It is possible that the astronomer region lies entirely in the part of scientists that is not shopkeeper. So this need not be true. Conclusion I does not follow. Step 4: Check Conclusion II: Some shopkeepers are astronomers. From the statements we do not know that any of the scientists who are shopkeepers are astronomers. They may all be scientists who are not astronomers. So this also does not have to be true. Conclusion II does not follow. Step 5: Check Conclusion III: Some shopkeepers are scientists. This is exactly what Statement 2 says in another wording. If some scientists are shopkeepers, then some shopkeepers are scientists. Hence Conclusion III definitely follows. Step 6: Check Conclusion IV: All scientists are astronomers. Statement 1 only says that all astronomers are scientists, not the other way around. There can be scientists who are not astronomers. So Conclusion IV does not follow. Verification / Alternative check: We can quickly verify by building an example. Suppose there are 10 scientists, of which 2 are astronomers and 3 are shopkeepers, but none of the astronomers are shopkeepers. In that case Statement 1 and Statement 2 are both satisfied. In this scenario, it is still true that some shopkeepers are scientists, but astronomers are not shopkeepers and not all scientists are astronomers. This confirms that only Conclusion III is forced to be true in all valid cases. Why Other Options Are Wrong: - Options that include Conclusion I wrongly assume that all astronomers are among the shopkeepers, which is not guaranteed. - Options that include Conclusion II assume that at least one shopkeeper is definitely an astronomer, which is not forced by the statements. - Options that include Conclusion IV assume that every scientist must be an astronomer, but the given data never states this. - The option that claims that the answer cannot be determined ignores the fact that Conclusion III directly restates Statement 2. Common Pitfalls: Many students reverse or overextend universal statements. From all astronomers are scientists they incorrectly jump to all scientists are astronomers. Another common mistake is to assume that some scientists are shopkeepers automatically implies some shopkeepers are astronomers, without checking the overlap carefully. Always remember that some does not specify which members of the larger group are involved. Final Answer: Therefore, the only conclusion that definitely follows from the given statements is Only conclusion III follows.

Question 7

Read the following two statements about teachers, actors, and women. Treat both statements as logically true, even if they seem unrealistic in everyday life, and then decide which of the given conclusions follow logically from them.  Statement 1: Al…

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Introduction / Context: This logical reasoning question deals with categorical statements about teachers, actors, and women. You are asked to ignore real world experience and instead treat the given statements as perfectly true in a mathematical sense. The goal is to decide which conclusions must hold in every possible situation that satisfies the statements, and which conclusions are only possibilities or are completely wrong. Given Data / Assumptions: - Statement 1: All teachers are actors. Every teacher belongs to the set of actors. - Statement 2: Some actors are women. At least one actor is a woman. - No extra links between teachers and women are explicitly given. - Conclusions I to IV are to be tested strictly against the above statements. Concept / Approach: When we read All teachers are actors, we interpret it as the set of teachers lying fully inside the set of actors. The phrase Some actors are women means there is at least one person who is both an actor and a woman. To validate a conclusion, we must be sure it is true in every possible diagram that fits the statements. If we can draw even one valid diagram where the conclusion fails, then that conclusion does not logically follow. This is the standard Venn diagram and counterexample approach for syllogism problems. Step-by-Step Solution: Step 1: Draw a large circle for actors. Inside it, draw a smaller circle for teachers to show that all teachers are actors. Step 2: Mark an overlapping region between actors and women, because some actors are women. However, the problem does not say that these women are teachers. Step 3: Conclusion I states that all teachers are women. For this to be true, the entire teacher circle must lie within the women circle. The given statements never say this, so this conclusion does not necessarily follow. Step 4: Conclusion II states that some women are teachers. The fact that some actors are women does not guarantee that any of the teacher actors are among those women. It is possible that the women who are actors are not teachers. So this conclusion also does not necessarily follow. Step 5: Conclusion III states that some women are actors. This is exactly what Statement 2 asserts. Therefore Conclusion III definitely follows. Step 6: Conclusion IV states that all actors are teachers. The original statement only says that all teachers are actors, not that every actor is a teacher. So this conclusion clearly does not follow. Verification / Alternative check: Imagine there are ten actors. Out of these, two are teachers and three are women, but none of the women are teachers. In this situation, all teachers are actors and some actors are women, so the statements are satisfied. However, not all teachers are women, not all actors are teachers, and no woman is a teacher. Still, some women are actors. This example confirms that only Conclusion III must be true. Why Other Options Are Wrong: - Any option that includes Conclusion I assumes every teacher is also a woman, which is not given. - Any option that includes Conclusion II assumes at least one woman teacher, again not supported by the data. - Any option that includes Conclusion IV reverses the first statement and wrongly claims that all actors are teachers. - The option claiming that none of the conclusions follows ignores Conclusion III, which directly comes from Statement 2. Common Pitfalls: A very common mistake is to reverse All A are B into All B are A. Another error is to assume that some actors are women automatically implies some women are teachers just because teachers are also actors. Never introduce extra links that are not explicitly or logically forced by the statements. Always rely on careful diagram based checking. Final Answer: Hence, the only conclusion that definitely follows is Only conclusion III follows.

Question 8

Consider the following statements about bags, pockets, and pouches. Assume that both statements are logically true and then decide which of the given conclusions definitely follow from them.  Statement 1: Some bags are pockets. Statement 2: No pocke…

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Introduction / Context: This problem is a classic example of syllogism involving the sets bags, pockets, and pouches. You must treat the given statements as absolutely true and then check which conclusions follow in every configuration that satisfies the statements. The focus is on understanding how some and no type statements interact to create necessary logical results. Given Data / Assumptions: - Statement 1: Some bags are pockets. At least one object is both a bag and a pocket. - Statement 2: No pocket is a pouch. The sets pockets and pouches do not overlap at all. - We assume the usual meaning of some as at least one. - Conclusions I and II must be tested strictly on the basis of these statements. Concept / Approach: The pattern Some A are B tells us that there exists at least one element which belongs to both set A and set B. The pattern No B is C means that sets B and C are completely disjoint. When a question combines such statements, the key is to track specific overlapping elements and see what must be true about them. If we can identify a particular object whose properties are forced by the statements, we can often verify or reject proposed conclusions directly. Step-by-Step Solution: Step 1: From Statement 1, there exists at least one item that is both a bag and a pocket. Call this item X. So X belongs to the intersection of bags and pockets. Step 2: From Statement 2, no pocket is a pouch. Therefore, any object that is a pocket cannot simultaneously be a pouch. Step 3: Since X is a pocket, and no pocket is a pouch, X cannot be a pouch. However, X is also a bag. Therefore, we have identified at least one bag that is not a pouch. This confirms Conclusion I: some bags are not pouches. Step 4: Now look at Conclusion II: some pockets are bags. Statement 1 says some bags are pockets. With some type statements, the order of the sets is reversible. If some bags are pockets, then the same element X also shows that some pockets are bags. So Conclusion II is also necessarily true. Step 5: There is no configuration consistent with the given statements in which Conclusion I or Conclusion II fails, because they are built directly from the guaranteed element in the intersection. Verification / Alternative check: As a quick check, construct a small example. Suppose there are five bags, and exactly one of them is also a pocket. Suppose further that there are some pouches, but none of the pockets are pouches. In that case, there is clearly one bag that is a pocket and that is not a pouch, so some bags are not pouches and some pockets are bags. This concrete example matches the reasoning above and confirms that both conclusions must follow. Why Other Options Are Wrong: - Any option claiming that only one of the conclusions follows ignores the direct logical link from the shared element between bags and pockets. - The option that states neither conclusion follows is incorrect because we can prove both using only the given statements, without any additional assumptions. - The option that says the result cannot be determined is also wrong, since the existence of the common element forces both conclusions. Common Pitfalls: Students sometimes fail to recognise that some A are B and some B are A are logically equivalent. Another mistake is to think that the presence of a negative statement like no pocket is a pouch makes everything uncertain. In fact, such a statement is very strong and can directly produce conclusions about elements that are known to be pockets. Final Answer: Therefore, both conclusions definitely follow, so the correct answer is Both conclusion I and conclusion II follow.

Question 9

Consider the following logical statements about teachers, followers, and famous people. Assume that each statement is logically true and then decide which of the given conclusions definitely follow.  Statement 1: Some teachers are followers. Stateme…

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Introduction / Context: This question deals with logical relationships among teachers, followers, and famous people. The problem uses some type statements, which indicate partial overlap between sets. You are required to determine which conclusions must hold in every situation that satisfies the given statements, not just in one possible picture. This is a standard test of your understanding of Venn diagram based reasoning for syllogism questions. Given Data / Assumptions: - Statement 1: Some teachers are followers. At least one person is both a teacher and a follower. - Statement 2: Some followers are famous. At least one person is both a follower and famous. - The statements do not directly link teachers to famous people. - Conclusions I and II must be checked strictly against these statements. Concept / Approach: When we see some A are B, we know there exists at least one element in the intersection of A and B. However, we are not told anything about other members of either set. Different some type statements involving the same middle set do not automatically guarantee a common element among all three sets. Thus we must carefully check whether a shared object is forced or whether it is only a possibility. A conclusion is valid only if it holds in every valid diagram that respects the statements. Step-by-Step Solution: Step 1: From Statement 1, mark at least one person who is both a teacher and a follower. This creates an overlap between the sets teachers and followers. Step 2: From Statement 2, mark at least one person who is both a follower and famous. This creates an overlap between followers and famous people. Step 3: Check Conclusion II first. Conclusion II says that some followers are teachers. This is simply a rewording of Statement 1. If some teachers are followers, then the very same individuals show that some followers are teachers. Therefore, Conclusion II definitely follows. Step 4: Now test Conclusion I, which states that some teachers are famous. For this to be forced, the same follower who is a teacher in Statement 1 would also need to be the follower who is famous in Statement 2. However, the statements do not require that the two overlaps refer to the same person. It is perfectly possible that the teacher follower is not famous, and that a different follower is famous. Step 5: Construct a counterexample: let one follower be a teacher but not famous, and let another follower be famous but not a teacher. Both statements are satisfied, but there is no person who is both teacher and famous. Hence Conclusion I does not necessarily follow. Verification / Alternative check: The counterexample method is enough to reject Conclusion I. Any valid syllogism must survive every possible diagram that respects the given statements. Since we can build at least one valid case where no teacher is famous, we know that Conclusion I is not logically guaranteed. In contrast, Conclusion II simply restates the overlap between teachers and followers and is therefore always true whenever Statement 1 is true. Why Other Options Are Wrong: - Options that include Conclusion I treat the overlaps as if they must involve the same individuals, which is not forced by the statements. - Any option that omits Conclusion II ignores the direct implication of Statement 1. - The option claiming that neither conclusion follows is incorrect because Conclusion II is a direct consequence of the first statement. - The option that says the answer cannot be determined is also wrong, since we have a definite logical result for Conclusion II. Common Pitfalls: A common error is to join some type statements through a middle term and assume transitivity. Students often think that if some teachers are followers and some followers are famous, then some teachers must be famous. This is not valid unless the question explicitly forces the same individual to appear in both overlaps. Always check whether a link is guaranteed or only possible. Final Answer: Therefore, the only conclusion that definitely follows is Only conclusion II follows.

Question 10

Read the following analytical statement about the selection of cricket teams and then decide which of the given conclusions can be logically drawn from it.  Statement: Selectors pick our cricket teams based on regional considerations instead of on p…

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Introduction / Context: This question is from the area of statement and conclusion in logical reasoning. The statement comments on how cricket teams are selected and connects this selection method to difficulty in winning Test series. You must carefully distinguish between what is actually asserted and what is merely suggested or emotionally appealing. Logical questions of this kind check whether you can separate strong conclusions from exaggerated interpretations. Given Data / Assumptions: - Selectors pick teams based on regional considerations rather than pure merit. - As a result, it becomes difficult for the teams to win Test series against other countries. - The statement talks about difficulty, not impossibility. - No extra assumptions about the absolute strength or weakness of the team are allowed. Concept / Approach: In verbal reasoning, a conclusion is said to follow if it is a logical consequence of the statement, not just a possible opinion. We also need to differentiate between phrases such as difficult, impossible, and hopeless. Saying that something is difficult does not mean it can never happen. Likewise, if a cause is identified for a problem, it may hint at a possible solution, but we must check whether the solution is actually implied by the text. We must check each conclusion against this standard. Step-by-Step Solution: Step 1: Focus on the key part of the statement: selection based on regional considerations, instead of pure merit, makes it difficult to win Test series. Step 2: Analyse Conclusion I: Our teams have no hope of winning Test series. The statement does not say that victory is impossible. It only says that it is difficult. Something can be difficult yet still achievable. Therefore Conclusion I overstates the situation and does not logically follow. Step 3: Analyse Conclusion II: Our cricket teams need to be selected on pure merit. The statement directly suggests that selection based on factors other than merit is the reason for the difficulty in winning. If the cause of the problem is non merit based selection, then the natural logical remedy is that teams should be selected on pure merit to improve performance. Step 4: Since the statement criticises regional selection in contrast to pure merit, it clearly indicates that merit based selection is desirable or necessary for better chances of success. Hence Conclusion II can be logically drawn. Step 5: There is nothing in the statement that supports the extreme hopelessness asserted in Conclusion I, so we cannot accept it. Verification / Alternative check: Imagine that team selection is changed. If selectors start choosing players purely on performance and fitness, the difficulty mentioned in the statement would likely reduce. This supports the idea that the original statement implicitly recommends selection on merit. However, even with poor selection, an occasional victory is still possible due to luck or individual brilliance, so it would be wrong to claim that there is no hope at all. This confirms the rejection of Conclusion I and acceptance of Conclusion II. Why Other Options Are Wrong: - The option including only Conclusion I fails because it misinterprets difficult as impossible. - The option that includes both conclusions treats the hopelessness in Conclusion I as if it were stated, which it is not. - The option that rejects both conclusions ignores the clear recommendation that team selection should focus on merit. - The option that claims the answer cannot be determined is incorrect, because the author explicitly contrasts regional considerations with pure merit in a negative tone. Common Pitfalls: Students often get carried away by the emotional tone of such statements and jump to extreme conclusions. It is important to read carefully and respect the exact strength of the words used. Difficult does not mean impossible, and criticism of a practice usually hints at the need to change that practice, not at total hopelessness. Logical reasoning rewards calm, precise reading rather than emotional reaction. Final Answer: Thus, only the second conclusion logically follows from the given statement, so the correct answer is Only Conclusion II follows.

Question 11

Consider the following logical statements about plants, trees, and the colour green. Assume that both statements are true and then decide which of the given conclusions definitely follow.  Statement 1: All plants are trees. Statement 2: No tree is g…

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Introduction / Context: This question checks your understanding of categorical logic with universal statements and their implications. We have two strong statements about plants, trees, and the colour green. The challenge is to see what they force us to accept, and also what they do not say. In particular, we must avoid reading extra meaning into phrases like all and none, and we must be careful with apparently tricky phrases like plants which are not trees. Given Data / Assumptions: - Statement 1: All plants are trees. Every plant belongs to the set of trees. - Statement 2: No tree is green. The sets trees and green objects do not overlap at all. - There is no mention of any plant that is not a tree. - Conclusions I and II must be tested only against these statements. Concept / Approach: From the statement All plants are trees, we know the set of plants is fully inside the set of trees. From No tree is green, we know that no member of the tree set can be green. Consequently, no plant can be green, because every plant is a tree. However, the second conclusion talks about plants which are not trees, which is actually an empty group under the first statement. In standard reasoning questions, we usually do not draw specific conclusions about an empty set unless it is explicitly handled. Step-by-Step Solution: Step 1: Visualise a large circle representing trees. Inside this circle, draw a smaller circle representing plants, because all plants are trees. Step 2: Now represent green objects as a separate region that does not intersect the tree circle at all, because no tree is green. Step 3: Since every plant lies inside the tree set, and no tree is green, it is impossible for any plant to be green. So the statement some plants are green is false in every situation that respects the given statements. Step 4: Therefore Conclusion I, which asserts that some plants are green, cannot follow. It is actually the opposite of what the combined statements imply. Step 5: Now consider Conclusion II: those plants which are not trees are green. Under Statement 1 there are no plants that are not trees. The phrase plants which are not trees refers to an empty group. Standard exam style syllogism treats this as something about a non existent category, so we cannot assert from the statements that such non existent plants are green. Step 6: Since the data does not confirm any actual green plant, and the group in Conclusion II is empty, neither of the two conclusions is logically forced by the given statements. Verification / Alternative check: An alternative way is to rephrase the information verbally. If every plant is a tree and no tree is green, then every plant is also not green. This directly contradicts Conclusion I. For Conclusion II, we note that the first statement has already ruled out the existence of a plant that is not a tree. The conclusion tries to assign the colour green to a group that does not exist according to the statements. Hence, it cannot be treated as a valid logical consequence in this exam setting. Why Other Options Are Wrong: - Options that include Conclusion I ignore the combined effect of the two statements, which actually eliminate green plants. - Options that include Conclusion II treat the phrase plants which are not trees as if that group is real, even though Statement 1 excludes it. - The either or option is incorrect because neither conclusion is supported, and there is no exclusive choice between them. - The cannot be determined option is wrong, because the statements are strong enough to show that both conclusions fail to follow. Common Pitfalls: Students sometimes misread All plants are trees as All trees are plants, which is not correct. Another trap is to misinterpret No tree is green as No green thing is a tree and then assume it says something about all non tree plants, which do not even exist under the first statement. Always respect the exact direction of universal statements and inspect whether the category discussed in a conclusion actually exists according to the premises. Final Answer: Thus, neither of the two conclusions follows from the given statements, so the correct answer is Neither Conclusion I nor Conclusion II follows.

Question 12

Consider the following statements about states, dams, and water problems. Treat the statements as logically true and then decide which conclusions definitely follow.  Statement: All states that have dams face no water problem. Statement: One of the …

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Introduction / Context: This statement and conclusion question connects the presence of dams in a state with the absence of water problems. You must interpret the statements in a purely logical manner and then evaluate the given conclusions. The question also introduces the phrase may be, which expresses possibility rather than certainty. Understanding how possibility based conclusions behave in logical reasoning is important here. Given Data / Assumptions: - Any state that has a dam faces no water problem. For such states the water situation is under control. - There is at least one state which has no dam. - Nothing is explicitly stated about the water situation in states without dams. - Conclusions I and II must be tested on this information only. Concept / Approach: The first statement is a universal conditional statement: having a dam implies no water problem. However, it does not say anything about states without dams. They might or might not have water problems. When a conclusion uses the phrase may be, it expresses that something is possible and not ruled out by the given data. If the information given allows a situation, we can often say that it may be so. Further, from a statement that links the presence of dams to the absence of water problems, we can interpret that dams are effective in solving or preventing water scarcity, which is the idea behind Conclusion II. Step-by-Step Solution: Step 1: From the first statement, we know that for every state with a dam, there is no water problem. So dams are associated with the removal or avoidance of water problems. Step 2: From the second statement, we know that there exists at least one state without a dam. However, nothing is specified about whether this state has a water problem or not. Step 3: Consider Conclusion I: the state without a dam may be facing a water problem. Since the premises do not guarantee the absence of water problems for states without dams, it is logically possible that such a state suffers from water scarcity. The conclusion does not claim certainty but only possibility. Therefore, this conclusion can be accepted as it is consistent with the given statements. Step 4: Now examine Conclusion II: dams solve the water problem. The first statement clearly connects having a dam with there being no water problem. This strongly supports the idea that dams are effective in solving or preventing water problems in states that have them. So Conclusion II also follows. Step 5: Together, the premises show that while states with dams do not face water issues, a state without a dam might or might not have a water problem. Hence both conclusions are compatible with the given information and follow logically. Verification / Alternative check: To verify, imagine two states. State A has a dam and no water problem. State B has no dam and is suffering from water shortage. This fits both statements and demonstrates Conclusion I, because the damless state is facing a problem. The same example shows that dams are associated with the absence of problems in State A, which supports Conclusion II. Since we can build such a consistent scenario and nothing in the statements contradicts it, both conclusions follow. Why Other Options Are Wrong: - An option that accepts only one conclusion ignores the full implications of the statements. - The option that rejects both conclusions fails to recognise that possibility based Conclusion I is not ruled out and that Conclusion II is directly supported. - The claim that the answer cannot be determined is inaccurate, because the first statement explicitly ties dams to the absence of water problems. Common Pitfalls: A frequent error is to assume that if dams remove water problems, then all states without dams definitely have water problems. The statements do not say this. Another mistake is to misunderstand the phrase may be as weak or unacceptable in logical reasoning. In fact, when the premises allow a situation and do not rule it out, a may be statement about that situation can be a valid conclusion. Final Answer: Thus, both conclusions are logically supported by the given statements, so the correct answer is Both conclusion I and conclusion II follow.

Question 13

Consider the following statements about fruits, leaves, and grapes. Assume that the statements are true and then decide which of the given conclusions definitely follow.  Statement 1: All fruits are leaves. Statement 2: Some fruits are grapes.  Conc…

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Introduction / Context: This question is a straightforward syllogism problem involving the sets fruits, leaves, and grapes. You are given one universal and one particular statement and asked to determine which conclusions are logically guaranteed. Such questions are common in competitive exams and test your ability to reason with set inclusion and partial overlap using simple Venn diagram ideas. Given Data / Assumptions: - Statement 1: All fruits are leaves. Every fruit lies inside the set of leaves. - Statement 2: Some fruits are grapes. At least one fruit is also a grape. - Conclusions refer to the relationships among leaves, grapes, and fruits. - No other information about leaves or grapes is provided. Concept / Approach: The universal statement All fruits are leaves means that the fruit circle is completely within the leaf circle. The particular statement Some fruits are grapes means that there exists at least one element that is both a fruit and a grape. When evaluating conclusions, we look for what must always be true given these relationships. If a conclusion can be false in even one diagram that satisfies the statements, it does not logically follow. Step-by-Step Solution: Step 1: Draw a large circle representing leaves. Inside it, draw a smaller circle representing fruits, because all fruits are leaves. Step 2: Now represent grapes. Since some fruits are grapes, we mark at least one region where the grape set intersects the fruit set. That region is therefore also inside the leaf set. Step 3: Check Conclusion I: Some leaves are grapes. We have already identified at least one object that is both a fruit and a grape, and all fruits are leaves. Therefore, that object is also a leaf. This means there exists at least one leaf that is a grape. Hence Conclusion I definitely follows. Step 4: Check Conclusion II: All grapes are fruits. The statements tell us only that some fruits are grapes, not that every grape must be a fruit. There may be grapes that are not fruits at all according to the given data, because nothing is said about grapes in general. Therefore, Conclusion II is not forced by the statements. Step 5: Since only the first conclusion must hold in every valid configuration, the correct logical result is that only Conclusion I follows. Verification / Alternative check: Construct a quick example. Suppose all fruits are leaves, and apples, oranges, and grapes are types of fruits. Let us assume that two of the fruits are grapes, while there also exist some grapes that are not considered fruits in this simplified model. In such a case, the statements are satisfied: all fruits are leaves and some fruits are grapes. However, not all grapes are fruits, because some grapes fall outside the fruit category in this hypothetical setup. This confirms that Conclusion II is not guaranteed, while Conclusion I remains true since some leaves are indeed grapes. Why Other Options Are Wrong: - Any option that includes Conclusion II overstates the information given about grapes. - The option stating that both conclusions follow is incorrect because we have shown a scenario where some grapes are not fruits. - The options that reject both conclusions or say that nothing can be determined ignore the direct and clear implication behind Some fruits are grapes combined with All fruits are leaves. Common Pitfalls: Many candidates confuse some with all and assume symmetry where it does not exist. Another typical mistake is to think that if some fruits are grapes, then grapes and fruits must be identical sets. This is not logically valid. Always remember that some only guarantees partial overlap and that universal statements must be read exactly as given. Final Answer: Therefore, only the first conclusion is logically guaranteed by the statements, so the correct answer is Only conclusion I follows.

Question 14

Read the following statements about stenographers, lazy people, and men. Assume that both statements are true and then decide which conclusions definitely follow.  Statement 1: All stenographers are lazy. Statement 2: Some men are stenographers.  Co…

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Introduction / Context: This question is another example of syllogism involving three sets: stenographers, lazy people, and men. The statements define how these sets are related, and you must find which conclusions are logically forced. Here, one statement is universal, and the other is particular. The problem checks whether you can correctly derive consequences from these and avoid reversing or overgeneralising them. Given Data / Assumptions: - Statement 1: All stenographers are lazy. Every member of the stenographer set is inside the lazy set. - Statement 2: Some men are stenographers. At least one man is a stenographer. - We are not told that all men are stenographers or that all lazy people are stenographers. - Conclusions I and II must be tested on this limited information. Concept / Approach: When we read All stenographers are lazy, we understand it as set inclusion: stenographers are a subset of lazy people. The statement Some men are stenographers places at least one man inside the stenographer set. From this, we can trace that man into the lazy set, because all stenographers are lazy. To validate a conclusion, we check if it holds in every possible configuration consistent with the statements. If a conclusion states more than what is guaranteed, it must be rejected. Step-by-Step Solution: Step 1: From Statement 2, there is at least one person who is both a man and a stenographer. Call this person X. Step 2: From Statement 1, every stenographer is lazy. Therefore, X, who is a stenographer, is also lazy. So X is a man and lazy, which directly implies that some men are lazy. Step 3: This confirms Conclusion II as correct, because it is exactly what we have deduced: there exists at least one man who is lazy. Step 4: Now examine Conclusion I, which states that all lazy people are men. This is much stronger than anything given. We only know that stenographers are lazy and that at least one stenographer is a man. There can be lazy women, lazy children, or lazy people in general who are not men and not stenographers. The statements do not restrict all lazy people to the group of men. Step 5: Since it is easy to imagine lazy people who are not men, and the statements do not rule them out, Conclusion I does not logically follow. Verification / Alternative check: As a quick verification, suppose there are 100 lazy people, of whom only 10 are stenographers and 5 of these stenographers are men. The remaining 90 lazy people could be women or children. In this scenario, all stenographers are still lazy and some men are stenographers, so the statements are true. However, it is clearly false that all lazy people are men. This concrete example reinforces that Conclusion I is invalid, while Conclusion II remains valid. Why Other Options Are Wrong: - Options that include Conclusion I assume that every lazy person must be male, which is not supported by the data. - The option that includes both conclusions fails because one of them clearly overstates the information given. - The option that rejects both conclusions ignores the direct chain from men to stenographers to lazy people that proves Conclusion II. - The cannot be determined option is incorrect, because we can definitely say that some men are lazy. Common Pitfalls: A common mistake is to reverse the universal statement and read All lazy people are stenographers or All lazy people are men from the given statements. Another error is to think that because a specific example exists, all members of a broader group must share the same property. In syllogism, you must always respect the direction and strength of each statement and avoid adding hidden assumptions. Final Answer: Thus, only the second conclusion is logically forced, so the correct answer is Only conclusion II follows.

Question 15

Consider the following statements about cars, buses, and caves. Assume that both statements are logically true and then decide which of the given conclusions definitely follow.  Statement 1: Some cars are buses. Statement 2: All cars are caves.  Con…

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Introduction / Context: This syllogism question uses three sets with somewhat unusual names: cars, buses, and caves. Despite the odd wording, it follows the same rules of categorical logic. One statement is particular, and the other is universal. You must identify which conclusions are logically guaranteed when both statements are treated as true. The aim is to combine set inclusion with partial overlap and then test each conclusion carefully. Given Data / Assumptions: - Statement 1: Some cars are buses. At least one object is both a car and a bus. - Statement 2: All cars are caves. Every car lies inside the set of caves. - There is at least one car because Statement 1 talks about some cars. - Conclusions I to IV speak about caves and their relation to buses and cars. Concept / Approach: The universal statement All cars are caves means that the car set is a subset of the cave set. The particular statement Some cars are buses gives us a non empty intersection of cars and buses. Because all cars are caves, every car bus object is automatically a cave as well. To test conclusions, we identify what must hold in every diagram that fits these relationships and what is only possible or even contradicts the statements. Step-by-Step Solution: Step 1: From Statement 1, mark at least one object that is both car and bus. Call this object X. Step 2: From Statement 2, every car is a cave. Therefore, X, being a car, is also a cave. So X belongs to the intersection of caves, cars, and buses. Step 3: Consider Conclusion II: some caves are buses. We have just identified X as a cave and a bus. Therefore, this conclusion definitely follows. Step 4: Consider Conclusion IV: some caves are cars. Since every car is a cave and we know from Statement 1 that there is at least one car, that car is also a cave. Thus some caves are cars, and Conclusion IV definitely follows. Step 5: Now test Conclusion I: some caves are not buses. The statements do not give us any information about caves that are not cars, and they do not say that all cars are buses. It is possible that every cave is either a bus or a car that is also a bus. It is also possible that some caves are not buses. Since both possibilities are allowed, we cannot say that some caves are not buses must be true. Hence Conclusion I does not follow. Step 6: Test Conclusion III: no cave is a bus. This clearly contradicts the existence of X, which is a cave and a bus. Therefore Conclusion III is definitely false and does not follow. Verification / Alternative check: To verify, assume there are three cars, all of which are caves. Suppose one of these cars is also a bus and there are no other buses. Then some cars are buses and all cars are caves, so both statements are satisfied. In this picture, there is at least one cave that is a bus and at least one cave that is a car. However, it may or may not be the case that some caves are not buses, depending on whether there are additional caves outside the car set. This confirms that only the second and fourth conclusions are guaranteed. Why Other Options Are Wrong: - Any option that includes Conclusion I treats a possible situation as if it were compulsory. - Any option that includes Conclusion III directly contradicts the established intersection between caves and buses. - The option that selects only one of the true conclusions ignores the other logical consequence. - The cannot be determined option is incorrect because we can clearly deduce the existence of at least one cave that is a bus and at least one cave that is a car. Common Pitfalls: One common error is to assume that some A are B implies some A are not B or some B are not A, which is not necessary. Another mistake is to think that because all cars are caves and some cars are buses, all caves must be buses. The statements never say that all caves are cars or that all caves are buses. Always focus on exactly what is stated and avoid adding extra assumptions. Final Answer: Thus, only the second and fourth conclusions follow from the given statements, so the correct answer is Only conclusions II and IV follow.

Question 16

Consider the following statements about flies, ants, and insects. Assume that both statements are logically true and then decide which of the given conclusions definitely follow.  Statement 1: Some flies are ants. Statement 2: All insects are ants. …

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Introduction / Context: This question examines your understanding of how particular and universal statements combine in syllogism. The sets involved are flies, ants, and insects. You must decide whether the conclusions about these sets are forced by the given statements. The key ideas are subset relations and the difference between some and all type claims. Given Data / Assumptions: - Statement 1: Some flies are ants. At least one fly is also an ant. - Statement 2: All insects are ants. Every insect lies inside the set of ants. - There is no direct statement about the relation between flies and insects. - Conclusions I and II must be tested using these two statements only. Concept / Approach: The statement Some flies are ants tells us about a non empty overlap between flies and ants. The statement All insects are ants tells us that insects form a subset of ants. A conclusion is valid only when it must hold for every possible situation that respects these two statements. If there is a valid arrangement where a conclusion is false, then the conclusion does not follow. We must beware of overgeneralising from some to all and of assuming extra links that the statements do not provide. Step-by-Step Solution: Step 1: Visualise three sets: flies, ants, and insects. From Statement 1, draw an overlapping region between flies and ants to represent some flies being ants. Step 2: From Statement 2, place the insect set entirely inside the ant set, because all insects are ants. Step 3: Check Conclusion I, which says all flies are ants. The first statement only tells us that some flies are ants. There may be flies that are not ants, because nothing in the statements forces every fly into the ant set. Therefore, we cannot say that all flies are ants. Conclusion I does not follow. Step 4: Check Conclusion II, which states that some ants are insects. Since all insects are ants, every insect is an ant. In most exam style reasoning, a universal statement of the form all insects are ants is understood to describe a real non empty class, so there exist some insects. Those insects are ants, which means some ants are insects. Step 5: Thus, Conclusion II must hold in any realistic model where insects actually exist. The question is framed in a real world context, so we treat the class of insects as non empty and accept that some ants are insects. Verification / Alternative check: To verify with an example, suppose there are 100 ants, of which 10 are insects and 20 are flies. Let 5 of the flies also be ants. This fits both statements: some flies are ants and all insects are ants. In this scenario, it is clearly false that all flies are ants, because there are flies outside the ant set. However, some ants are insects, since those 10 insects are all ants. This confirms that Conclusion II follows and Conclusion I does not. Why Other Options Are Wrong: - Options that include Conclusion I assume a universal statement about flies which is not given. - The option claiming that both conclusions follow is wrong because we have just seen a counterexample to Conclusion I. - The option that rejects both conclusions ignores the clear subset relation between insects and ants. - The cannot be determined option is incorrect because under normal exam conventions we treat the class insects as non empty, making Conclusion II logically valid. Common Pitfalls: Many candidates mistakenly convert Some A are B into All A are B, or they hesitate to accept conclusions involving some when a universal premise is present. It is also common to ignore the practical meaning of everyday sets like insects and treat them as possibly empty. In competitive exams, when such real world sets are used, they are normally understood to exist, which justifies conclusions like some ants are insects. Final Answer: Therefore, only the second conclusion is logically supported, and the correct answer is Only conclusion II follows.

Question 17

Consider the famous proverb based statement and the information about Sujatha. Treat the statements as logically true and then decide which conclusion definitely follows.  Statement 1: All that glitters is not gold. (This means that many glittering …

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Introduction / Context: This question combines a proverb like statement with a specific factual statement about a person. The proverb All that glitters is not gold is often misread or over interpreted. In logical reasoning, we must translate it carefully and then see whether it gives any information about gold objects themselves. The goal is to decide whether we can say anything definite about the glittering property of the ornament worn by Sujatha. Given Data / Assumptions: - Statement 1: All that glitters is not gold. Interpreted in everyday reasoning, this means that there are glittering objects that are not gold and that glittering appearance alone does not guarantee that something is gold. - Statement 2: Sujatha wears a gold ornament. - Nothing is said about whether gold ornaments in general glitter or do not glitter. - Conclusions I and II make opposite claims about the ornament worn by Sujatha. Concept / Approach: The proverb focuses on the idea that if something glitters, it may still not be gold. It warns us not to judge quality by appearance. It does not state a complete logical rule relating gold and glitter. In particular, it does not say that nothing that glitters can be gold or that all gold must or must not glitter. Therefore, we must be very cautious when trying to draw conclusions about a specific gold ornament based on this proverb like statement. Step-by-Step Solution: Step 1: Translate Statement 1 into logical language. The intended meaning is that glittering is not a reliable test for gold. There exist glittering things that are not gold. It is not a strict universal statement about all glittering objects being non gold. Step 2: From Statement 2 we know that Sujatha wears an ornament that is made of gold. However, nothing in either statement tells us whether gold ornaments glitter or not. Step 3: Check Conclusion I: the ornament worn by Sujatha glitters. This may be true in real life, but the given statements do not assert it. The fact that some glittering things are not gold says nothing about whether gold things glitter. Therefore, Conclusion I is not logically forced. Step 4: Check Conclusion II: the ornament worn by Sujatha does not glitter. This is again a claim without any support in the statements. The proverb does not say that gold objects never glitter. It only warns that glitter is not proof of gold. Step 5: Because we cannot deduce either glittering or non glittering behaviour of the ornament from the given information, neither conclusion is justified. Verification / Alternative check: Imagine two possible worlds. In the first world, Sujatha's gold ornament glittered because of polished metal and embedded stones. In the second world, the same ornament was dull or covered and did not glitter. In both worlds the proverb like statement All that glitters is not gold can still be true, because in both worlds there are other glittering objects, such as imitation jewellery, that are not gold. This shows that the status of the proverb does not determine whether Sujatha's ornament glitters. Hence neither conclusion can be forced from the statements. Why Other Options Are Wrong: - Options that select Conclusion I or Conclusion II assume extra information about gold ornaments that is not given. - The option that selects both conclusions is impossible, because they contradict each other and there is no support for either one. - The option that claims the answer cannot be determined is close to the correct intuition, but in this exam style framing, the precise logical result is that neither conclusion follows from the statements. Common Pitfalls: A major pitfall is to misread the proverb as All that glitters is never gold, which would be a very different and much stronger statement. Another mistake is to assume that gold always glitters and to project this real world belief into the logical analysis. In reasoning questions, we must ignore outside knowledge and stick only to what the statements say and what they clearly imply. Final Answer: Therefore, neither conclusion can be logically drawn from the given statements, so the correct answer is Neither Conclusion I nor Conclusion II follows.

Question 18

In the following question, two statements are given followed by two conclusions. Treat the statements as true, even if they seem to be at variance with commonly known facts, and then decide which of the conclusions definitely follow.  Statement 1: A…

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Introduction / Context: This question is a classic example of two step syllogism, where one term links clouds to fog and another links fog to white objects. You must determine which of the given conclusions are necessarily true if the statements are assumed to be absolutely correct. It is important to visualise the nested set structure and then examine how the conclusions arise from that structure. Given Data / Assumptions: - Statement 1: All clouds are fog. Every cloud lies inside the set of fog. - Statement 2: All fog is white. Every fog object lies inside the set of white objects. - We treat the existence of clouds and fog as real, non empty categories. - Conclusions I and II must be judged using only these statements. Concept / Approach: The first statement makes clouds a subset of fog, and the second makes fog a subset of white objects. Together, they yield a chain of inclusion: clouds inside fog and fog inside white things. From this chain, we can deduce that clouds are also white, and that clouds form part of the fog set. In syllogism problems, if A is a subset of B and B is a subset of C, then A is a subset of C. Also, because clouds are real, both fog and white sets are populated. This directly supports conclusions about some type relationships. Step-by-Step Solution: Step 1: From Statement 1, draw clouds as a subset of fog. This means every cloud is also fog. Step 2: From Statement 2, draw fog as a subset of white objects. Every fog element is white. Step 3: Combining these, clouds are a subset of fog, which is itself a subset of white. Therefore, every cloud is also white, and every cloud is a particular example of fog. Step 4: Check Conclusion II first: some fog is clouds. Since clouds are a subset of fog and clouds exist, there are fog elements that are clouds. Hence some fog is clouds is definitely true. Step 5: Check Conclusion I: some white things are clouds. We have already reasoned that clouds are also white. Since clouds exist, there are white objects that are clouds. This means that some white things are clouds is also definitely true. Step 6: Both conclusions talk about the existence of elements in intersections created by the subset relationships, and both are logically guaranteed by the given statements. Verification / Alternative check: To verify, consider an example. Suppose there are 10 clouds. By Statement 1, all of them are types of fog. By Statement 2, any fog must be white. Therefore, the 10 clouds are among the fog objects and also among the white objects. This directly shows that some fog is clouds and some white objects are clouds. The conclusions hold no matter how many other fog or white objects exist, as long as clouds exist and the chain of subsets is respected. Why Other Options Are Wrong: - Options that accept only one conclusion ignore the fact that both follow from the subset chain. - The option that rejects both conclusions contradicts the clear logical implications of the statements. - The option that claims the answer cannot be determined is incorrect because the existence of clouds and the subset relations are enough to make both conclusions certain. Common Pitfalls: A common error is to treat such problems mechanically without tracing the full set structure. Some candidates also confuse All A are B with All B are A, which leads to wrong conclusions. Here, however, the direction of both statements aligns to give a straightforward inclusion chain. Always visualise the sets to avoid confusion and to see which some type conclusions are guaranteed. Final Answer: Therefore, both conclusions logically follow from the given statements, so the correct answer is Both I and II follow.

Question 19

In the following question, two statements are given followed by two conclusions. Treat the statements as true, even if they appear to contradict common knowledge, and then decide which of the conclusions definitely follow.  Statement 1: All flowers …

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Introduction / Context: This syllogism question links flowers with leaves and plants. Two statements are provided, one universal and one particular. Your task is to decide whether each of the two conclusions follows logically. This type of problem is very common in logical reasoning sections of competitive exams and is best approached using simple set diagrams and careful reading of the statements. Given Data / Assumptions: - Statement 1: All flowers are leaves. Every flower belongs to the leaf set. - Statement 2: Some flowers are plants. At least one flower is also a plant. - Flowers clearly exist because Statement 2 talks about some flowers. - Conclusions I and II must be checked with only this information. Concept / Approach: The universal statement makes flowers a subset of leaves. The particular statement establishes an overlap between flowers and plants. Combining these, we can often derive overlaps between leaves and plants. In general, if all A are B and some A are C, then those some A are both B and C, so some B are C and some C are A. This pattern directly applies here. We just need to confirm it with a step by step analysis. Step-by-Step Solution: Step 1: From Statement 1, draw the flower circle completely inside the leaf circle. This means every flower is also a leaf. Step 2: From Statement 2, mark an overlap between flowers and plants. There is at least one object that is both flower and plant. Step 3: Since every flower is a leaf, the flower plant object is also a leaf. Therefore there is at least one object that is both a leaf and a plant. This directly supports Conclusion I: some leaves are plants. Step 4: The same element also shows that some plants are flowers, because it is both plant and flower. This directly supports Conclusion II. Step 5: Both conclusions are tied to the existence of that common element connecting flowers, leaves, and plants and are therefore logically guaranteed. Verification / Alternative check: For an intuitive check, imagine that roses, lilies, and marigolds are flowers. Suppose all flowers are classified as leaves in this abstract model. Also assume that some flowers, say roses, are plants. Then roses are simultaneously flowers, leaves, and plants. This shows that some leaves are plants and that some plants are flowers. Any other elements in the sets will not change these overlaps as long as the original statements remain true. Why Other Options Are Wrong: - Options that accept only one of the conclusions ignore the symmetry created by the common element that is both flower and plant. - The option that rejects both conclusions contradicts the direct consequence of the subset relation combined with the some type overlap. - The cannot be determined option is incorrect because we have clear evidence for both conclusions from the given statements alone. Common Pitfalls: A frequent error is to treat some as vague and think that almost nothing can be deduced from it. In truth, some gives very useful information about overlap. Another mistake is to ignore the subset relation and consider flowers, leaves, and plants as unrelated. Always start by putting all given statements into a consistent diagram and then read the conclusions from that picture. Final Answer: Thus, both conclusions definitely follow from the given statements, so the correct answer is Both I and II follow.

Question 20

In the following question, two statements are given followed by two conclusions. Treat the statements as true, even if they appear to be at variance with common sense, and then decide which of the conclusions definitely follow.  Statement 1: All daw…

Accepted Answer

Introduction / Context: This question involves three time related sets: dawn, day, and night. The statements tell us how these sets relate to each other, and the conclusions test your understanding of negative universal relationships. You must decide which conclusion follows necessarily if both statements are accepted as logically true, without bringing in your own knowledge about real world time periods. Given Data / Assumptions: - Statement 1: All dawn is day. The set dawn is entirely inside the set day. - Statement 2: No day is night. There is no overlap between day and night. - The existence of dawn and day is assumed in the context of the problem. - Conclusions I and II must be checked strictly against these statements. Concept / Approach: The statement No day is night tells us that the sets day and night do not intersect. In logic, the statement No A is B is equivalent to No B is A. Hence, from No day is night, we can also say No night is day. The first conclusion captures this direct equivalence. The first statement All dawn is day puts dawn entirely inside day, and because day does not intersect night, dawn also cannot intersect night. This will help us test the second conclusion that claims some dawn is night. Step-by-Step Solution: Step 1: Visualise the set day and the set night as two disjoint circles, because No day is night. Step 2: Place the set dawn as a smaller circle completely inside the day circle, because All dawn is day. Step 3: Examine Conclusion I: No night is day. If no element of day is night, then there is no element that belongs to both day and night. The relationship is symmetric, so night and day do not overlap in either direction. Thus No night is day is equivalent to No day is night and definitely follows. Step 4: Examine Conclusion II: Some dawn is night. Since all dawn is inside day and day has no overlap with night, dawn also has no overlap with night. Therefore, it is impossible for any part of dawn to be night. The conclusion that some dawn is night contradicts the given statements. Step 5: Because Conclusion I is a valid restatement of the second statement and Conclusion II contradicts the set diagram, only the first conclusion follows. Verification / Alternative check: To verify, imagine marking points on a time line. Let the period labelled day have no intersection with the period labelled night, in line with Statement 2. Place dawn strictly within the day period. In such an arrangement, it is immediately clear that nothing in night can be day and nothing in dawn can be night. This confirms that the first conclusion is correct while the second is impossible under the given premises. Why Other Options Are Wrong: - Any option that accepts Conclusion II fails to respect the fact that day and night are disjoint sets. - The option claiming both conclusions are true is wrong because the second conclusion contradicts the set relations. - The option that rejects both conclusions ignores the direct equivalence between No day is night and No night is day. - The cannot be determined option is incorrect because the statements are strong enough to decide the status of both conclusions. Common Pitfalls: Some students misinterpret No A is B as only one directional and hesitate to accept the reverse No B is A. Others try to use real life intuition about dawn, day, and night, rather than treating the terms as abstract sets. In exam style logical reasoning, you must rely only on the structural relationships stated in the problem and not on your personal understanding of time or nature. Final Answer: Therefore, only the first conclusion is logically supported, so the correct answer is Only conclusion I follows.

Statement and Conclusion Questions