Question 1

Two women A and B are shopping in a mall. They start from the same point in the mall and walk in different directions as described below.  Woman A walks 150 m towards the West, then turns to her left and walks 160 m. Woman B walks 140 m towards the …

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Introduction / Context: This is a standard directions and distance problem in logical reasoning. Two women start from the same point and walk different paths with several turns. You must carefully track each displacement in terms of East West and North South components and then compute the final relative position of B with respect to A. Such questions test your ability to interpret directional language and perform simple coordinate style calculations. Given Data / Assumptions: - Both A and B start from exactly the same point in the mall. - Woman A walks 150 m West, then turns left and walks 160 m. span style="display:block;">- Woman B walks 140 m East, then 160 m South, then turns left and walks 120 m. - Left turns are taken relative to the current facing direction. - We assume standard orientation: North up, South down, East to the right, West to the left. Concept / Approach: A convenient approach is to imagine a coordinate system with the starting point as the origin. We treat East as the positive x direction and North as the positive y direction. West becomes negative x and South becomes negative y. Every movement can be broken into horizontal and vertical components. At the end, we subtract A's final coordinates from B's final coordinates to know where B is with respect to A. The magnitude of the difference gives us the distance, while the sign gives us the direction. Step-by-Step Solution: Step 1: Start with woman A. From the origin, she walks 150 m West. That corresponds to a movement of minus 150 along the x axis and zero along the y axis. Step 2: A then turns left from West. Facing West, a left turn means she now faces South. She then walks 160 m South, which is a change of minus 160 along the y axis. So A's final coordinates are x = -150 and y = -160. Step 3: Now track woman B. From the origin, she walks 140 m East. That is plus 140 along the x axis. Step 4: B then turns South and walks 160 m. This step changes the y coordinate by minus 160, leaving x at plus 140. Step 5: B then turns left from facing South. A left turn from South makes her face East. She walks 120 m East, which adds 120 to the x coordinate. So B's final coordinates are x = 140 + 120 = 260, y = -160. Step 6: Now compute B's position relative to A. A is at (-150, -160) and B is at (260, -160). The relative displacement from A to B is 260 minus ( -150 ) along x and equal y coordinates, which is 410 m in the East direction. The vertical difference is zero. Verification / Alternative check: An alternative way is to compare horizontal movements directly. Across the entire journey, A has gone 150 m West, while B has gone 140 m East plus an additional 120 m East, for a total of 260 m East. The net separation in the East West direction between them is 260 m East plus 150 m East, which gives 410 m East from A to B. Since both moved 160 m South after their first turn, their vertical positions match. Therefore B lies exactly 410 m to the East of A and at the same North South level. Why Other Options Are Wrong: - Options suggesting 170 m difference result from incorrect subtraction of East and West movements instead of adding them to find separation. - Options that place B to the West of A ignore the fact that B has moved net East while A has moved net West. - The cannot be determined option is invalid because the distances and directions are fully specified. Common Pitfalls: A very common mistake is to misinterpret left turn directions when a person is not facing North initially. For example, from West a left turn takes you South, not North. Another error is mixing up net displacement from the origin with relative displacement between two points. Always track each path systematically and then compute the difference between final positions when the question asks where one person is with respect to another. Final Answer: Hence, woman B is located 410 m East of A.

Question 2

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 conclusion definitely follows.  Statement 1: Some cle…

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Introduction / Context: This logical reasoning question deals with three groups of people: clever, intelligent, and smart. You are given two short statements and asked which conclusions must follow if both statements are accepted as completely true. This is a classic syllogism pattern where you must carefully track overlaps and exclusions between sets and avoid adding any extra assumptions. Given Data / Assumptions: - Statement 1: Some clever persons are intelligent. This means at least one person is both clever and intelligent. - Statement 2: No intelligent person is smart. This means that the sets intelligent and smart do not overlap at all. - Conclusion I: Some intelligent persons are clever. - Conclusion II: Some smart persons are clever. - We must decide which conclusion is forced by the two statements. Concept / Approach: The phrase some A are B means there is at least one element that belongs to both set A and set B. The statement no B is C tells us that sets B and C are completely disjoint. A conclusion is valid only if it must be true in every possible diagram that satisfies the given statements. If we can imagine even one valid diagram where a conclusion fails, that conclusion does not follow. Step-by-Step Solution: Step 1: From Statement 1, mark at least one person who is both clever and intelligent. Call this person X. So X lies in the intersection of the clever set and the intelligent set. Step 2: Statement 2 says that no intelligent person is smart. Therefore, the intelligent set and the smart set do not intersect at all. Step 3: Consider Conclusion I: some intelligent persons are clever. This is simply a rewording of Statement 1. If some clever persons are intelligent, then those same persons are also intelligent and clever. Therefore, some intelligent persons are clever. Conclusion I definitely follows. Step 4: Now consider Conclusion II: some smart persons are clever. From Statement 2 we only know that intelligent and smart do not overlap. We are not told anything about clever persons who are not intelligent. It is possible that some smart persons are clever, but it is equally possible that none of the clever persons are smart. Step 5: Because both possibilities are allowed by the statements, Conclusion II is not guaranteed. There may be a diagram where no clever person is smart, which would make Conclusion II false. Therefore Conclusion II does not follow. Verification / Alternative check: Imagine an example. Suppose there are clever people A and B, and intelligent people include A, but no intelligent person is smart. Also assume that all smart people are different individuals C and D, who are neither clever nor intelligent. In this situation, some clever persons are intelligent, and no intelligent person is smart, so both statements hold. However, there is no smart person who is clever. This confirms that Conclusion I is valid while Conclusion II is not forced by the given information. Why Other Options Are Wrong: - Any option that includes Conclusion II treats a mere possibility as if it were a necessity. - The option that says both conclusions follow is incorrect because Conclusion II can be false in a valid diagram. - The option that rejects both conclusions ignores the fact that Conclusion I restates the overlap given directly in Statement 1. - The cannot be determined option is wrong because we can clearly and certainly accept Conclusion I. Common Pitfalls: A common mistake is to assume that if some clever persons are intelligent and no intelligent person is smart, then clever and smart must overlap or cannot overlap in a particular way. In reality, the problem gives no information about clever persons who are not intelligent. Another pitfall is failing to notice that Conclusion I is simply the same information as Statement 1 expressed from the other side of the overlap. Final Answer: Thus, only the first conclusion is logically guaranteed. The correct answer is Only conclusion I follows.

Question 3

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 commonly known facts, and then decide which conclusion definitely follows.  Statement 1: Some w…

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Introduction / Context: This syllogism problem connects the sets wild animals, carnivores, and lions. You are given one particular statement and one universal statement and must decide which conclusions are logically forced. The question checks whether you can move correctly through subset relationships and avoid overstating what the premises allow. Given Data / Assumptions: - Statement 1: Some wild animals are carnivores. At least one wild animal is also a carnivore. - Statement 2: All wild animals are lions. Every wild animal lies inside the set of lions. - Conclusion I: All carnivores are lions. - Conclusion II: Some lions are carnivores. - No further information about carnivores in general is provided. Concept / Approach: The statement all wild animals are lions means that the wild animal set is a subset of the lion set. The statement some wild animals are carnivores gives us a non empty intersection between wild animals and carnivores. Because every wild animal is a lion, any wild animal that is a carnivore is also a lion. This allows us to derive at least one lion that is a carnivore. However, nothing in the statements tells us that every carnivore must be a lion, because there could be carnivores that are not wild animals. Step-by-Step Solution: Step 1: From Statement 2, draw a circle for lions and place the wild animal circle completely inside it, because all wild animals are lions. Step 2: From Statement 1, mark at least one element that lies in the intersection of wild animals and carnivores. Call this element X. This means X is wild and X is a carnivore. Step 3: Since every wild animal is a lion, X is also a lion. So X is a lion and X is a carnivore. Therefore, there exists at least one lion that is a carnivore. This directly supports Conclusion II: some lions are carnivores. Step 4: Now look at Conclusion I: all carnivores are lions. The given information only tells us that some wild animals are carnivores and that all wild animals are lions. It does not say that all carnivores are wild. There may be carnivores that are not wild animals, such as domestic dogs or other animals outside the wild classification. These carnivores need not be lions. Step 5: Since it is easy to imagine carnivores outside the wild animal set, and nothing in the statements rules them out, we cannot say that every carnivore is a lion. Conclusion I does not follow. Verification / Alternative check: Consider a concrete example. Suppose there are ten wild animals, all of which are lions. Among these ten, four are carnivores. Also suppose there exist other carnivores, such as domestic dogs, which are not wild animals and not lions in this imagined world. In this case, some wild animals are carnivores and all wild animals are lions, so both statements are satisfied. However, not all carnivores are lions, because the domestic dogs in the example are carnivores but not lions. Still, some lions are carnivores because those four wild carnivores are lions. This confirms that only Conclusion II is guaranteed. Why Other Options Are Wrong: - Any option that includes Conclusion I assumes more than what the statements provide about all carnivores. - The option that accepts both conclusions is incorrect because Conclusion I can fail in a valid scenario. - The option that rejects both conclusions ignores the direct deduction that at least one lion is a carnivore. - The cannot be determined option is not correct because we have a clear logical path supporting Conclusion II. Common Pitfalls: Students often confuse partial overlap with total inclusion and jump from some A are B to all B are A. Another common error is to treat the term wild as if it covers all carnivores, when the statements leave room for carnivores that are not wild. Always read each quantifier carefully and avoid reversing the direction of universal statements. Final Answer: Therefore, only the second conclusion is logically supported by the given statements. The correct answer is Only conclusion II follows.

Question 4

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

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Introduction / Context: This is a standard syllogism question involving everyday terms: wheat, grain, and flour. The two statements describe how these three sets are related. Your task is to decide whether each of the two conclusions must be true whenever the statements are true. This type of problem is very common in exams and is usually solved by thinking in terms of simple set diagrams. Given Data / Assumptions: - Statement 1: All wheat is grain. The set wheat is completely inside the set grain. - Statement 2: Some wheat is flour. At least one part of wheat is also flour. - Conclusion I: Some grain is flour. - Conclusion II: Some flour is wheat. - We assume that the classes wheat and flour are non empty, since the second statement refers to some wheat as flour. Concept / Approach: From all wheat is grain we know that every unit of wheat that exists is a type of grain. From some wheat is flour we know that there is at least one item that simultaneously belongs to the sets wheat and flour. Because that item is wheat, it is also grain. Thus we can derive overlaps between grain and flour and between flour and wheat. A conclusion about some type overlap is valid if the existence of such an element is guaranteed by the statements. Step-by-Step Solution: Step 1: Draw a large circle for grain. Inside it, draw a smaller circle for wheat, because all wheat is grain. Step 2: From Statement 2, mark at least one point that lies both in the wheat circle and in the flour set. This point represents wheat that has been ground into flour. Step 3: Since this point lies in the wheat set and wheat is fully inside the grain set, the same point automatically lies in the grain set. Therefore, there exists at least one item that is both grain and flour. This supports Conclusion I: some grain is flour. Step 4: The same point shows that at least one item is both flour and wheat. That is exactly what Conclusion II says: some flour is wheat. Therefore Conclusion II also definitely follows. Step 5: Both conclusions are based on the same overlapping element created by the combination of the two statements. Hence both conclusions must be true whenever the statements are true. Verification / Alternative check: Take a simple real world analogy. Imagine a sack that contains only wheat. By Statement 1, everything in that sack is grain. Now suppose some of that wheat is milled into flour as per Statement 2. That milled part is still wheat by source, still grain by category, and now also flour by processed form. So that portion is simultaneously grain, wheat, and flour. It clearly shows that some grain is flour and some flour is wheat. No variation in the remaining grain or flour can change this basic fact as long as the two statements hold. Why Other Options Are Wrong: - Options that accept only one conclusion ignore the obvious symmetry in the overlapping element. - The option that rejects both conclusions contradicts the direct logical implication of the overlap between wheat, grain, and flour. - The cannot be determined option is incorrect because the existence of wheat that is flour is enough to guarantee both conclusions. Common Pitfalls: Students sometimes underestimate the power of a some type statement and believe that no further conclusion can be drawn. Others misread all wheat is grain as all grain is wheat, which is the reverse and not given. In this question the information is very clear and concrete, so it is a good reminder that simple statements can still yield definite and strong conclusions. Final Answer: Therefore, both conclusions logically follow from the given statements. The correct answer is Both I and II follow.

Question 5

In the following question, two statements are given, each followed by two conclusions. Treat the statements as true, even if they appear to be at variance with everyday experience, and then decide which of the conclusions definitely follow.  Stateme…

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Introduction / Context: This question involves three overlapping sets: children, adults, and old people. Two some type statements are given, and you are asked to decide which negative conclusions, if any, must follow. The task is to see whether the existence of some overlaps forces the existence of specific non overlapping elements, or whether such elements remain only possible and not certain. Given Data / Assumptions: - Statement 1: Some children are adults. At least one person belongs to both the children set and the adult set. - Statement 2: Some adults are old. At least one adult is also old. - There may be other children, adults, or old people, but they are not described explicitly. - Conclusion I: Some children are not old. - Conclusion II: Some adults are not old. Concept / Approach: The key idea is that some simply guarantees existence of at least one element with the stated property. It does not say anything about the rest of the set. The fact that some adults are old does not tell us whether other adults are or are not old. Similarly, knowing that some children are adults does not tell us whether those particular children are old or not old. Negative conclusions require clear information about the absence of overlap, which is not given here. Step-by-Step Solution: Step 1: From Statement 1, mark at least one person who is both a child and an adult. Call this person X. This shows that the sets children and adults overlap. Step 2: From Statement 2, mark at least one adult who is old. Call this person Y. This shows that the sets adults and old people overlap. Step 3: Notice that the problem does not say whether X and Y are the same person or different persons. Both possibilities are allowed. X may be old or not old, and Y may or may not be a child. Step 4: Consider Conclusion II first: some adults are not old. For this to be necessarily true, there must be at least one adult who is definitely not old in every valid diagram. However, it is possible that every adult is old. In that scenario, the statement some adults are old is still true, but there is no adult who is not old. Since such a diagram is consistent with the statements, Conclusion II is not guaranteed. Step 5: Now consider Conclusion I: some children are not old. It is possible that every child, including those who are adults, is old. That would satisfy both statements, because there could be at least one child who is an old adult and at least one adult who is old. In that case, there would be no child who is not old. So Conclusion I is also not guaranteed. Step 6: Because we can construct valid diagrams where both conclusions fail, neither conclusion follows logically from the given statements. Verification / Alternative check: Construct a specific example. Suppose there are three people, all of whom are adults and all of whom are old. Two of them are also classified as children in this abstract setting. Then, some children are adults (true) and some adults are old (true). However, in this example, every child is old and every adult is old. There is no child who is not old and no adult who is not old. This concrete scenario shows that both conclusions can be false while the statements remain true, which proves that neither conclusion is logically forced. Why Other Options Are Wrong: - Any option that accepts Conclusion I assumes there must be at least one child outside the old group, which is not stated. - Any option that accepts Conclusion II assumes there must be at least one adult outside the old group, which again is not stated. - The option that says both conclusions follow is clearly incorrect, since the example above shows both can fail at the same time. - The cannot be determined option is not appropriate here, because in syllogism we ask whether something must follow. Since these conclusions do not have to be true, the correct logical status is that neither follows. Common Pitfalls: Many candidates assume that some automatically implies some not, for example that if some adults are old then some adults are not old. This is not valid. It is always possible that every adult is old and the some statement still remains true. Another error is to bring in real world knowledge about the meanings of child and adult instead of treating them as abstract sets in this logical exercise. Final Answer: Thus, neither conclusion is logically compelled by the given statements. The correct answer is Neither I nor II follows.

Question 6

In the following logical reasoning problem, two statements are given about men, saints and sinners. You must treat both statements as true and then decide which of the given conclusions, if any, logically follows from them: Statements: (I) Men are s…

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Introduction / Context: This question tests basic syllogism skills. You are given two simple universal statements about men, saints and sinners. Your task is to see which conclusion necessarily follows from these statements, assuming they are perfectly true, even if they disagree with everyday beliefs or moral views. Given Data / Assumptions: Statement I: Men are sinners. Statement II: Saints are men. Conclusion I: Saints are sinners. Conclusion II: Sinners are saints. All terms refer to sets or groups of people. Concept / Approach: In syllogism, a statement like men are sinners means every member of the set men belongs to the set sinners. Similarly, saints are men means every saint belongs to the set men. By combining such subset relations, we can see what other subset relations must hold. However, we must be careful not to reverse the direction of inclusion, because that usually creates invalid conclusions. Step-by-Step Solution: Step 1: Translate statement I into set language: all men are sinners. The set of men is completely contained inside the set of sinners. Step 2: Translate statement II: all saints are men. The set of saints is completely contained inside the set of men. Step 3: Combine the two: if all saints are men and all men are sinners, then every saint is also a sinner. This is a direct chain of inclusion: saints ⊂ men ⊂ sinners. Step 4: Therefore conclusion I, saints are sinners, must be true whenever both statements are true. Step 5: Consider conclusion II, sinners are saints. This would mean the set of sinners is contained inside the set of saints. The given statements do not say this. They only say saints are a subset of men and men are a subset of sinners. Step 6: It is possible to have many sinners who are not saints at all. So conclusion II does not logically follow. Verification / Alternative check: Imagine an example. Suppose there are 100 men, all of whom are sinners. Out of these, only 10 are saints. Then every saint is a man and every man is a sinner. That matches the statements. In this picture, the 10 saints are sinners, so conclusion I holds. But there are 90 other sinners who are not saints, so it is false that all sinners are saints. This shows that conclusion II is not forced by the statements. Why Other Options Are Wrong: Option B claims only conclusion II follows, which is incorrect because conclusion II can easily be false while the statements remain true. Option C says neither conclusion follows, but we have seen that conclusion I must always hold. Option D says both conclusions follow, which wrongly includes conclusion II. Option E suggests that exactly one of the two follows without specifying, but the question and option wording require you to identify the specific correct conclusion, which is conclusion I only. Common Pitfalls: A common mistake is to mix up all A are B with all B are A. From men are sinners you cannot say all sinners are men. Similarly, from saints are men you cannot say all men are saints. Always keep track of the direction of the arrow in subset relations. Drawing a simple Venn diagram often helps to avoid this confusion. Final Answer: The correct logical result is that only conclusion I follows, that is, saints are sinners.

Question 7

In this syllogism question, two statements are given about rings, bangles and gold. You must treat both statements as true and then decide which of the given conclusions, if any, logically follow: Statement I: No rings are bangles. Statement II: All…

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Introduction / Context: This problem is a standard syllogism exercise based on set relations. You are given two statements connecting rings, bangles and gold. Using these, you must decide which conclusions definitely follow, assuming that the statements are fully true in the exam sense of syllogistic reasoning. Given Data / Assumptions: Statement I: No rings are bangles. Statement II: All gold are rings. Conclusion I: No bangles are gold. Conclusion II: Some rings are gold. We work under exam conventions where the named classes (like gold) are treated as existing. Concept / Approach: No rings are bangles means that the sets rings and bangles are completely disjoint. All gold are rings means that the set of gold objects lies entirely inside the set of rings. From these subset and disjoint relations, we can derive further relations among gold, rings and bangles. In many competitive exams, if all gold are rings, it is also accepted that some rings are gold (because the class gold is treated as non empty). Step-by-Step Solution: Step 1: From statement I, rings and bangles do not overlap at all. There is no object that is both a ring and a bangle. Step 2: From statement II, every gold item is a ring. The set gold is a subset of the set rings. Step 3: Combine the two. If all gold items are rings, and no ring is a bangle, then no gold item can be a bangle. So there is no bangle that is gold, which supports conclusion I: no bangles are gold. Step 4: Under usual exam assumptions, the category gold is not empty. So if all gold are rings, there is at least one ring that is gold. That gives some rings are gold, which matches conclusion II. Step 5: Therefore both conclusion I and conclusion II are treated as logically following from the given statements in the context of such reasoning questions. Verification / Alternative check: Construct a simple model. Let rings be {r1, r2, r3}, bangles be {b1, b2}, and gold be {r1, r2}. All gold (r1 and r2) are rings, and no rings are bangles because the sets {r1, r2, r3} and {b1, b2} are disjoint. Here, no bangle is gold, so conclusion I holds. Also, some rings (r1 and r2) are gold, so conclusion II also holds. It is not possible in this typical exam setting to satisfy the statements and make either of the conclusions false. Why Other Options Are Wrong: Option A claims that only conclusion I follows, ignoring the standard inference some rings are gold. Option B selects only conclusion II and ignores the clear disjointness between bangles and gold implied by the statements. Option D says neither conclusion follows, which is clearly incorrect. Option E suggests that exactly one follows, but we have just seen that both are simultaneously forced by the statements under normal exam assumptions. Common Pitfalls: A frequent mistake is to reverse the direction of statements like all gold are rings and treat them as if all rings are gold, which is not given. Another pitfall is to think that from all gold are rings we cannot say anything about specific ring gold elements. However, in standard exam syllogism, named sets such as gold are taken to contain at least one member, so some rings are gold is considered valid. Final Answer: The correct reasoning is that both conclusion I and conclusion II follow from the given statements.

Question 8

In this logical reasoning question, two factual statements about a DRDO Smart Anti Airfield Weapon test are given. Treat both as true and decide which of the given conclusions, if any, logically follow from them: Statement I: The DRDO has tested the…

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Introduction / Context: This problem is a statement and conclusions question based on a defence news type context. Two brief statements describe a test of a Smart Anti Airfield Weapon. You must decide which of the two given conclusions necessarily follow from these statements, assuming the statements are fully true but not adding any extra information from outside knowledge. Given Data / Assumptions: Statement I: The Defence Research and Development Organisation has tested the Smart Anti Airfield Weapon from an Indian Air Force aircraft. Statement II: The lightweight high precision guided bomb is one of the world class weapons systems. Conclusion I: The DRDO Chairman Dr. S. Christopher congratulated the DRDO and Indian Air Force teams for the successful mission. Conclusion II: The test was carried out by the Aircraft and System Testing Establishment of the Indian Air Force. We must check logical necessity, not real world plausibility or likelihood. Concept / Approach: In statement and conclusion questions, a conclusion follows only if it must be true in every possible situation where the given statements are true. If we can imagine even one situation in which the statements hold but a conclusion is false, that conclusion does not logically follow. Extra details, names of people, and specific units or organisations often indicate information that goes beyond the given statements. Step-by-Step Solution: Step 1: Examine conclusion I. The statements mention DRDO, the weapon, and an Indian Air Force aircraft but say nothing about any chairman, congratulations or messages. Step 2: It is entirely possible that the test was successful but that no public congratulations were recorded, or that someone else conveyed them. Therefore conclusion I is not forced by the statements. Step 3: Examine conclusion II. The statements say the test involved an Indian Air Force aircraft, but they do not specify which unit carried out the test. Step 4: The Aircraft and System Testing Establishment is one possible unit, but the statements do not mention it. The test could have been carried out by some other squadron or testing unit. Step 5: Since both conclusions add details that are not contained in the statements, neither is logically compelled. Verification / Alternative check: Imagine one scenario where the statements are true: DRDO and the Indian Air Force conduct a test flight of the weapon using a regular operational squadron aircraft, and the mission report simply notes success without any formal congratulatory message from the chairman. In this case, both statements are still true, but conclusion I is false and conclusion II may also be false if another unit conducted the test. This shows that neither conclusion must follow from the given information. Why Other Options Are Wrong: Option A and option D each assume that one of the conclusions is guaranteed, which adds details about persons or specific establishments not stated in the premises. Option B treats both conclusions as following, which is even stronger and clearly unsupported. Option E suggests that exactly one of them must be true, but we have seen scenarios where both could be false while the original statements remain true. Common Pitfalls: A common mistake is to rely on outside knowledge about typical defence testing procedures or news reports, for example remembering that certain units often perform such tests or that senior officials usually send congratulations. In reasoning questions, you must ignore such external information and base your answer strictly on the given text. Final Answer: The logically correct evaluation is that neither conclusion I nor conclusion II follows from the given statements.

Question 9

In this syllogism question, two statements link pizzas, pancakes and bread. Treat both statements as true and decide which of the conclusions, if any, logically follow: Statement I: Some pizzas are pancakes. Statement II: All bread are pizzas. Concl…

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Introduction / Context: This is a classic set based reasoning problem. The two statements describe how the sets pizzas, pancakes and bread are related. From this, you must determine whether either of the suggested conclusions is forced to be true. As always, you must ignore real world food knowledge and treat the statements as purely logical descriptions. Given Data / Assumptions: Statement I: Some pizzas are pancakes. Statement II: All bread are pizzas. Conclusion I: All pancakes are bread. Conclusion II: No bread are pizzas. Some means at least one but not necessarily all. Concept / Approach: A statement like some pizzas are pancakes means there is at least one object that belongs to both sets pizzas and pancakes. All bread are pizzas means that the entire set bread is contained inside the set pizzas. To test each conclusion, you should try to draw a Venn diagram or construct simple examples and see whether it is possible for the statements to be true while the conclusion is false. If that is possible, then the conclusion does not logically follow. Step-by-Step Solution: Step 1: Interpret statement I: the sets pizzas and pancakes overlap in at least one element. Step 2: Interpret statement II: the set bread lies completely inside the set pizzas. Step 3: Check conclusion I, all pancakes are bread. The statements do not restrict where pancakes can lie except that some of them overlap with pizzas. Pancakes can exist outside bread, outside pizzas, or anywhere else consistent with some pizzas being pancakes. Step 4: Therefore it is possible to draw a picture where some pizzas are pancakes, all bread are pizzas, but many pancakes are not bread. So conclusion I is not forced. Step 5: Check conclusion II, no bread are pizzas. This directly contradicts statement II, which says all bread are pizzas. If all bread are pizzas, it cannot be true that no bread are pizzas. Step 6: Hence conclusion II definitely does not follow and is actually inconsistent with the premises. Verification / Alternative check: Take a concrete example. Let pizzas be {p1, p2, p3}, pancakes be {p2, pan1} and bread be {p1}. Statement I holds because p2 is both a pizza and a pancake. Statement II holds because all bread items (p1) are pizzas. However, not all pancakes are bread because pan1 is a pancake that is not bread, so conclusion I fails. Also bread (p1) is a pizza, so conclusion II, which claims no bread are pizzas, is clearly false. This confirms that neither conclusion is logically valid. Why Other Options Are Wrong: Option A chooses conclusion I, which is not forced by the premises. Option B chooses conclusion II, which actually contradicts the second statement. Option C says both follow, which is impossible since one conclusion directly clashes with the statements. Option E suggests that exactly one of them must follow, but we have found situations in which both fail while the statements remain true. Common Pitfalls: A common mistake is to treat some pizzas are pancakes as if it were all pizzas are pancakes or all pancakes are pizzas. Another error is to overlook direct contradictions between statements and conclusions, as happens with conclusion II. Always rewrite statements carefully, use arrows or Venn diagrams, and test potential counterexamples. Final Answer: The correct reasoning shows that neither conclusion I nor conclusion II follows from the given statements.

Question 10

In this environmental reasoning question, two statements are given about water pollution and its causes. Treat both statements as true and decide which of the given conclusions, if any, logically follow: Statement I: The water pollutants are rising …

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Introduction / Context: This problem deals with water pollution and industrialisation. You are given two general statements about rising pollutants and the main causes of pollution. Then you are asked to check which conclusion about industrial behaviour and concern for future generations is logically supported by these statements. Given Data / Assumptions: Statement I: Water pollutants are rising slowly and spoiling the sanctity of water. Statement II: The main cause of water pollution is industrialisation and lack of a sustainable approach towards the environment. Conclusion I: Industries are mixing all left over slurries into nearby water bodies causing immense pollution. Conclusion II: Future generations need to be considered before engaging in pollution causing activities. The word main indicates a primary cause, not necessarily that every industry behaves in one extreme way. Concept / Approach: In statement and conclusion questions, we look for conclusions that are reasonably and directly suggested by the given information. Very specific statements about exact behaviour, such as all industries mixing every slurry into rivers, must have solid backing in the premises. Broader value based conclusions about sustainable thinking often follow when the statements highlight long term environmental harm and poor approaches to sustainability. Step-by-Step Solution: Step 1: From the two statements we know that water quality is deteriorating and that the main reasons are industrialisation and lack of sustainable environmental practices. Step 2: Consider conclusion I, which says industries are mixing all the left over slurries into nearby water bodies. The statements do not mention slurry, mixing behaviour, or that all industries act in exactly this way. Step 3: It is possible that many industries discharge waste into water, but it is also possible that some pollution comes from air deposition, agricultural runoff, or badly treated effluents rather than direct dumping of all slurries. Thus the statements do not force conclusion I. Step 4: Consider conclusion II. If the main causes are industrialisation and lack of sustainable approach, then clearly current activities are harming the environment and spoiling water for the future. Step 5: It is reasonable and natural to infer that, to address this, people and industries should think about the interests of future generations before carrying out pollution causing activities. This conclusion flows from the idea of sustainability mentioned in the statements. Verification / Alternative check: Think in terms of policy guidance. The statements describe a situation where present practices are unsustainable and damaging. A standard conclusion drawn in such contexts is that decision makers must consider long term impacts on future generations. However, the specific claim that all industries are mixing all slurry into water bodies is a narrow, extreme behaviour that is not supported by the broad description of industrialisation as a main cause. Therefore, choosing only conclusion II as following fits the style of exam questions on course of action and environment. Why Other Options Are Wrong: Option B claims that both conclusions follow, but we have seen that conclusion I is too specific and not backed by the premises. Option C says that neither follows, ignoring the strong suggestion of sustainable thinking and care for future generations in the context of environmental damage. Option D picks only conclusion I, which is clearly unjustified. Option E suggests that exactly one of them follows without clarifying which; the exam expects you to identify conclusion II explicitly as the correct one. Common Pitfalls: A common mistake is to treat every real world plausible statement as a valid conclusion. While it is realistic that some industries dump waste into water, the logical question is whether the premises explicitly support that exact behaviour in the extreme way described. Another pitfall is to underestimate broad normative conclusions such as the need to think about future generations, which are often the intended inferences in environment and sustainability questions. Final Answer: The logically supported view is that only conclusion II follows from the given statements.

Question 11

In this syllogism style question, two statements are given about authors, teachers and ladies. Treat both statements as true and decide which of the given conclusions, if any, logically follow: Statement I: Some authors are teachers. Statement II: N…

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Introduction / Context: This is a logical relations question about the sets authors, teachers and ladies. You must use the two given statements, treat them as completely true, and decide which of the two conclusions must hold. The problem checks whether you correctly interpret negative statements like no teacher is a lady and partial statements like some authors are teachers. Given Data / Assumptions: Statement I: Some authors are teachers. Statement II: No teacher is a lady. Conclusion I: Some teachers are not ladies. Conclusion II: Some ladies are not teachers. Some indicates existence of at least one member in the relevant intersection. Concept / Approach: Some authors are teachers means there is at least one person who is both an author and a teacher. No teacher is a lady means that the sets teachers and ladies are completely disjoint. We must see what these facts imply about the existence of teachers who are not ladies and about ladies who are not teachers. A conclusion follows only if it is impossible for the statements to be true and the conclusion false at the same time. Step-by-Step Solution: Step 1: From statement I, we know that teachers exist because some authors are teachers. So there is at least one teacher. Step 2: From statement II, no teacher is a lady. That means all teachers lie outside the set of ladies. Step 3: Combine the two. Since at least one teacher exists and no teacher is a lady, it follows that at least one teacher is not a lady. This is exactly what conclusion I states. Step 4: Now examine conclusion II: some ladies are not teachers. The statements do not actually assert that any lady exists. They only tell us that the sets teachers and ladies do not overlap. Step 5: It is logically possible, in pure set terms, that there are no ladies at all. In that extreme case, some ladies are not teachers would be false, while the given statements would still be true. Step 6: Because we can imagine a scenario with zero ladies and thus no element satisfying conclusion II, that conclusion is not logically forced by the premises. Verification / Alternative check: Construct a simple model. Let teachers be {t1}, authors be {t1, a1} and ladies be an empty set {}. Statement I is satisfied because some authors (t1) are teachers. Statement II is satisfied because no teacher is in the empty set of ladies. In this model, conclusion I holds because t1 is a teacher who is not a lady. But conclusion II fails because there are no ladies at all, so we cannot say some ladies are not teachers. This confirms that only conclusion I follows logically. Why Other Options Are Wrong: Option B chooses only conclusion II, which is not guaranteed. Option C says neither conclusion follows, ignoring the clear implication that at least one teacher is not a lady. Option D claims both follow, but we have shown that conclusion II can be false in a model where the statements hold. Option E suggests that exactly one of them (without specifying) must follow, but the exam expects you to identify conclusion I as the only valid one. Common Pitfalls: One common mistake is to assume that categories like ladies must contain some members just because the word is used, and then derive some ladies are not teachers from the disjointness. Formal logic does not automatically assume non empty sets unless specified. Another pitfall is to overlook the explicit existence provided by some authors are teachers, which guarantees that teachers exist and leads directly to conclusion I. Final Answer: The correct logical result is that only conclusion I follows from the given statements.

Question 12

In this reasoning problem, two statements are given about women, voting and politicians. Treat both statements as true and then decide which of the given conclusions, if any, logically follow: Statement I: No women can vote. Statement II: Some women…

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Introduction / Context: This question examines your ability to avoid making assumptions that are not supported by the given statements. The statements restrict voting rights for women and provide information about women politicians. You must then judge whether anything can be concluded about male politicians and politicians in general with respect to voting. Given Data / Assumptions: Statement I: No women can vote. Statement II: Some women are politicians. Conclusion I: Male politicians can vote. Conclusion II: Some politicians can vote. No additional facts about men or voting rules for men are provided. Concept / Approach: The statements provide only negative information about women and partial information about politicians. We know that some politicians are women who cannot vote, but nothing is said about male politicians or whether any politician at all possesses voting rights. A conclusion follows only if it must be true in every scenario where the statements hold. If we can imagine a scenario where the statements are true but a conclusion is false, that conclusion does not logically follow. Step-by-Step Solution: Step 1: From statement I, we know that the entire set women lies outside the set of voters. No woman belongs to the set of people who can vote. Step 2: From statement II, some women are politicians. That means there exists at least one politician who is a woman and therefore cannot vote. Step 3: The statements say nothing about men. They do not say that men can vote or that male politicians have any special rights. Step 4: Therefore, conclusion I, male politicians can vote, is not supported. It could be true or false depending on laws that the statements do not describe. Step 5: Consider conclusion II, some politicians can vote. At this point we know that at least some politicians are women who cannot vote. We have no information about whether any politicians are men or whether those men, if they exist, have voting rights. Step 6: It is possible that all politicians are women and none can vote. In such a scenario, both statements remain true, but conclusion II would be false. Hence conclusion II is not logically forced. Verification / Alternative check: Construct a concrete example. Let the set of women be {w1, w2}, the set of men be {m1, m2}, and the set of politicians be {w1, w2}. Suppose the law says no one at all can vote. Then no women can vote and some women are politicians, so both statements are true. However, no politician can vote and there are no male politicians at all. So conclusion I is false and conclusion II is also false. This shows that neither conclusion follows logically from the premises. Why Other Options Are Wrong: Option A selects conclusion I, but we have no basis to assert that male politicians can vote. Option B selects conclusion II, but we can easily imagine a world where all politicians are non voting women. Option D says both conclusions follow, which is even less justified. Option E suggests that one but not both must follow, but both can fail as demonstrated by the example, so this option is also incorrect. Common Pitfalls: Students often import their real world knowledge that in most societies men can vote and some politicians can vote. Such general knowledge cannot be used in this type of formal logic question. Another pitfall is to assume that if some women are politicians and women cannot vote, then there must be some male politicians who can vote to keep politics meaningful. This is again an outside assumption, not part of the statements. Final Answer: The logically sound conclusion is that neither conclusion I nor conclusion II follows from the given statements.

Question 13

In this syllogism question, two statements are given about birds, trees and hens. Treat both statements as true and decide which of the conclusions, if any, logically follow: Statements: (I) All birds are trees. (II) Some trees are hens. Conclusions…

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Introduction / Context: This question presents a deliberately unrealistic set relation among birds, trees and hens to focus purely on logical structure. You must treat the statements as literal set relations and decide which of the two conclusions are logically forced when those statements are true. Given Data / Assumptions: Statement I: All birds are trees. Statement II: Some trees are hens. Conclusion I: Some birds are hens. Conclusion II: Some hens are trees. We ignore real world biology and accept the statements as abstract set relations. Concept / Approach: All birds are trees means the entire set birds lies within the set trees. Some trees are hens means that there is a non empty intersection between the sets trees and hens. From this, we can decide whether there must be an overlap between birds and hens (conclusion I) and whether there must be hens that are trees (conclusion II). A conclusion follows only if there is no way for the statements to be true and that conclusion false at the same time. Step-by-Step Solution: Step 1: Translate statement I into set form: birds ⊂ trees. Every bird is a kind of tree. Step 2: Translate statement II: some trees are hens. So the intersection of trees and hens is non empty. Step 3: Consider conclusion II first. Some hens are trees is simply another way of stating that some trees are hens. These two statements are logically equivalent; they describe the same overlap from different directions. Step 4: Therefore conclusion II must follow from statement II. Step 5: Now examine conclusion I: some birds are hens. For this to be forced, the intersection of birds and hens would have to be non empty in every model that satisfies the statements. Step 6: The statements do not say that the particular trees which are hens are also birds. The hens that are trees might all lie in the part of trees that does not contain birds. Step 7: So it is possible that birds form one subset of trees, hens form another overlapping subset of trees, and these two subsets do not overlap at all. In that case, some birds are hens would be false while both statements remain true. Verification / Alternative check: Construct a simple diagram. Let trees be {t1, t2}, birds be {t1} and hens be {t2}. Then all birds (t1) are trees, so statement I holds. Some trees (t2) are hens, so statement II holds. However, there is no element that is both a bird and a hen, so conclusion I fails. At the same time, some hens (t2) are trees, so conclusion II is true. This shows that conclusion II follows but conclusion I does not. Why Other Options Are Wrong: Option A selects conclusion I, which is not forced since a counterexample exists. Option C says neither conclusion follows, but conclusion II follows directly from statement II. Option D says both follow, which is too strong. Option E suggests that exactly one of the two follows without specifying which, but the question format expects you to identify conclusion II explicitly as the correct one. Common Pitfalls: A frequent mistake is to assume that if two sets both lie partly inside a third set, then they must overlap each other. This is not necessarily true: two disjoint circles can both lie inside a larger circle. Another pitfall is to overlook that some trees are hens is logically identical to some hens are trees, but does not say anything about birds directly. Final Answer: The correct logical assessment is that only conclusion II follows from the given statements.

Question 14

In this set relation question, two statements are given about fans, cups and pillows. Treat both statements as true and decide which of the conclusions, if any, logically follow: Statements: (I) All fans are cups. (II) All cups are pillows. Conclusi…

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Introduction / Context: This is a straightforward syllogism problem about set inclusion. Two universal statements tell you how the sets fans, cups and pillows are nested. You must decide which of the given conclusions about fans and pillows logically follow from those nesting relations. Given Data / Assumptions: Statement I: All fans are cups. Statement II: All cups are pillows. Conclusion I: All fans are pillows. Conclusion II: All pillows are fans. All refers to universal inclusion, meaning complete containment of one set in another. Concept / Approach: The two statements form a simple chain: fans ⊂ cups ⊂ pillows. When one set is contained inside a second, and the second is contained inside a third, then the first is also contained inside the third. This transitivity allows us to deduce whether all fans are pillows. However, we must be careful not to reverse the direction of inclusion and claim that all pillows are fans, which usually does not follow. Step-by-Step Solution: Step 1: From statement I, all fans are cups. So every fan lies in the set cups. Step 2: From statement II, all cups are pillows. So every cup lies in the set pillows. Step 3: Combine these: any fan is a cup, and any cup is a pillow. Therefore any fan must also be a pillow. This proves conclusion I. Step 4: Now examine conclusion II, all pillows are fans. This would mean that the set pillows is contained inside the set fans. Step 5: The statements only say that fans are a subset of cups and cups are a subset of pillows. They do not restrict pillows to be only fans; pillows could include many other things besides fans. Step 6: So conclusion II is not guaranteed by the premises. Verification / Alternative check: Create an example. Let fans be {f1, f2}, cups be {f1, f2, c1} and pillows be {f1, f2, c1, p1}. All fans are cups and all cups are pillows. Conclusion I holds because every fan (f1, f2) is included among the pillows. But conclusion II is false because there is a pillow p1 that is not a fan. This confirms that only conclusion I follows from the statements. Why Other Options Are Wrong: Option B chooses conclusion II, which reverses the set inclusion and is not implied. Option C says neither conclusion follows, ignoring the simple transitive relation that supports conclusion I. Option D claims both follow, which would require pillows and fans to be exactly the same set, something not stated. Option E suggests that exactly one of them must follow, but the exam expects you to point out specifically that it is conclusion I that follows. Common Pitfalls: Students often confuse all A are B with all B are A. Here, all cups are pillows does not mean all pillows are cups. Another pitfall is to read too quickly and assume that if a small set is contained in a larger one, the larger set might also be contained in the smaller one. Visualising the sets as concentric circles helps keep the direction of inclusion clear. Final Answer: The correct logical conclusion is that only conclusion I follows from the given statements.

Question 15

In this reasoning question, two statements are given about men, education and family size. Treat both statements as true and decide which of the conclusions, if any, logically follow: Statements: (I) Some men are educated. (II) Educated persons pref…

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Introduction / Context: This question links the concepts of education and preference for small families. Using two simple statements, you must decide whether either conclusion about education of all families or the preferences of some men can be logically derived. This is a common pattern in syllogism and analytical reasoning sections of exams. Given Data / Assumptions: Statement I: Some men are educated. Statement II: Educated persons prefer small families. Conclusion I: All families are educated. Conclusion II: Some men prefer small families. Some means at least one; all indicates universal inclusion. Concept / Approach: Some men are educated means that the intersection between men and educated persons is non empty. Educated persons prefer small families means that every educated person belongs to the set of people who prefer small families. From these, we can find out if there must exist at least one man who prefers a small family. At the same time, we must check whether we can make any statement about all families being educated people, which appears much stronger and less directly connected. Step-by-Step Solution: Step 1: From statement I, choose at least one man, call him M, who is educated. Step 2: Statement II says that every educated person prefers small families. Since M is educated, M prefers small families. Step 3: Therefore there exists at least one man who prefers small families. This means some men prefer small families, which matches conclusion II. Step 4: Now examine conclusion I, all families are educated. The given statements say that educated persons prefer small families, not that every small family belongs to an educated person, or that all family members are educated. Step 5: The statements do not even mention the education level of all people, or whether families without educated members exist. So we cannot claim that all families are educated. Step 6: Therefore conclusion I does not follow from the statements. Verification / Alternative check: Construct an example. Let men be {m1, m2}, educated persons be {m1, e1}, and the set of people who prefer small families be {m1, e1, p1}. Then some men (m1) are educated, and all educated persons (m1 and e1) prefer small families. Thus some men (m1) prefer small families, so conclusion II holds. At the same time, there could be many families with uneducated members, such as p1 and others not in the educated set. So it is clearly false to say that all families are educated, and conclusion I fails. Why Other Options Are Wrong: Option A chooses conclusion I, which is not supported. Option C says neither conclusion follows, ignoring the direct chain from some men are educated to some men prefer small families. Option D claims both follow, which is incorrect because conclusion I does not. Option E suggests that exactly one of them must follow without specifying which; the exam expects you to identify conclusion II explicitly as the valid one. Common Pitfalls: A common error is to misread educated persons prefer small families as small families are always formed by educated persons, which reverses the direction of implication. Another pitfall is to overlook the word some, which guarantees existence of at least one educated man and therefore at least one man with the stated preference. Final Answer: The logically correct evaluation is that only conclusion II follows from the given statements.

Question 16

In this set based reasoning question, two statements are given about papers, files and pens. Treat both statements as true and decide which of the conclusions, if any, logically follow: Statements: (I) All paper are files. (II) Some files are pens. …

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Introduction / Context: This problem checks your understanding of partial and complete set relationships. Two statements describe how the sets paper, files and pens are related. You must decide whether either of two conflicting conclusions about papers and pens is forced by those statements. Given Data / Assumptions: Statement I: All paper are files. Statement II: Some files are pens. Conclusion I: No paper is a pen. Conclusion II: Some papers are pens. Paper refers to all sheets treated as a single set; files and pens are abstract sets as well. Concept / Approach: All paper are files means that the set paper lies entirely inside the set files. Some files are pens means there is at least one element that is both a file and a pen. However, the statements do not specify whether the paper objects are inside or outside that overlapping region of files and pens. To test each conclusion, we must see whether the statements force paper to avoid pens completely or force at least some paper to fall into the overlap with pens. Step-by-Step Solution: Step 1: Draw the set of files and place the set paper completely inside it to represent all paper are files. Step 2: Represent some files are pens by drawing the set pens so that it intersects the set files in a non empty region. Step 3: Check conclusion I, no paper is a pen. This would require that the entire set paper lies in the part of files that is outside pens. Step 4: It is possible to draw the diagram so that paper lies entirely outside the overlapping region, satisfying the statements and making conclusion I true. But it is also possible to place some or all of paper inside the overlap between files and pens, still satisfying the statements. Step 5: Check conclusion II, some papers are pens. This would require that at least part of the set paper lies in the overlap with pens. Step 6: As noted, there are valid diagrams where no paper lies in the overlap and diagrams where some paper lies in it. Therefore, the statements do not force either extreme; both kinds of arrangements are possible. Verification / Alternative check: Construct two examples. In example one, let files be {f1, f2, f3}, pens be {f3, p1}, and paper be {f1}. Then all paper (f1) are files, and some files (f3) are pens. Here, no paper is a pen, so conclusion I is true and conclusion II is false. In example two, let paper be {f3} instead, keeping the other sets the same. Now paper (f3) is both a file and a pen, so some papers are pens, conclusion II is true and conclusion I is false. The fact that both patterns are possible shows that neither conclusion is logically forced by the statements alone. Why Other Options Are Wrong: Option A asserts conclusion I, but we have seen a situation where conclusion II holds instead and the statements remain true. Option B asserts conclusion II, but example one shows that conclusion II can fail. Option D claims both conclusions follow, which is impossible because the conclusions contradict each other. Option E suggests an exclusive either or, but the logical task is to identify which conclusions must always hold, and the answer is that neither is guaranteed. Common Pitfalls: A typical mistake is to assume that if some files are pens and all paper are files, then automatically some papers are pens. This ignores the possibility that paper occupies the non overlapping part of files. Another pitfall is to jump to the opposite extreme and assume that paper must avoid pens, making conclusion I seem attractive. Always test with small concrete examples before deciding. Final Answer: The correct logical result is that neither conclusion I nor conclusion II follows from the given statements.

Question 17

In this reasoning question on furniture demand, two statements are given about wooden furniture and its replacement by fibre or plastic furniture. Treat both statements as true and decide which of the conclusions, if any, logically follow: Statement…

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Introduction / Context: This problem involves interpreting statements about changes in market demand for furniture. Two statements describe the decline in demand for wooden furniture and its replacement by fibre or plastic furniture. You must decide whether the given reasons about maintenance and handling properties logically follow from those statements. Given Data / Assumptions: Statement I: Demand for wooden furniture has gone down in an aggregate scenario. Statement II: Wooden furniture has been replaced by fibre or plastic furniture. Conclusion I: Wooden furniture needs more maintenance and is difficult to handle. Conclusion II: Plastic furniture is termite free and can be easily handled. We treat the statements as factual market observations, not as full explanations. Concept / Approach: The two statements talk about observed demand and substitution in the market, but they do not explicitly state the reasons behind these changes. Conclusions I and II provide specific causal explanations: higher maintenance and difficulty of handling for wooden furniture, and termite free and easy handling properties of plastic furniture. In logical reasoning questions, we can only accept such conclusions if they are clearly and directly implied by the premises. Step-by-Step Solution: Step 1: From the statements, we can infer that consumers are buying less wooden furniture and more fibre or plastic furniture compared to before. Step 2: However, the statements do not specify why this shift is occurring. Possible reasons could include price, fashion, supply, weight, durability, or any combination of factors. Step 3: Conclusion I asserts a specific reason: wooden furniture needs more maintenance and is difficult to handle. While this might be true in some cases, it is not mentioned in either statement and is not logically forced. Step 4: Conclusion II claims that plastic furniture is termite free and easy to handle. These are again plausible features, but the statements do not explicitly say that these properties are the reason for replacement. Step 5: Because neither conclusion is a necessary logical consequence of the given statements, we cannot accept them as following logically. Verification / Alternative check: Imagine an alternative cause for the trend: suppose wooden furniture has become more expensive due to higher timber costs, while plastic furniture is cheaper and more fashionable. This alone could explain the shift in demand, even if wooden furniture were easy to maintain and plastic furniture had some handling disadvantages. In this situation, both statements are still true, but neither conclusion about maintenance and termites is required. This shows that the conclusions are speculative and not logically implied. Why Other Options Are Wrong: Option A chooses only conclusion II, but we have no direct evidence for it in the premises. Option B claims that both conclusions follow, which adds two separate causal stories not supported by the data. Option D selects only conclusion I, again without textual backing. Option E suggests that exactly one of the two must follow, but we have seen that both can fail while the given statements remain valid. Common Pitfalls: A frequent error is to inject real world knowledge and personal experience, for example thinking that plastic furniture is obviously termite proof or that wooden furniture obviously needs more care, and then treating these assumptions as logically proven. Another pitfall is to confuse correlation with causation: the fact that plastic furniture demand rose while wooden furniture demand fell does not prove specific detailed reasons unless they are clearly stated. Final Answer: The logically correct assessment is that neither conclusion I nor conclusion II follows from the given statements.

Question 18

In this syllogism question with quantifiers, two statements are given about crops, machines and fools. Treat both statements as true and then decide which of the conclusions, if any, logically follow: Statements: (I) Most crops are machines. (II) So…

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Introduction / Context: This question uses deliberately absurd categories crops, machines and fools to force you to think purely about logical form. One statement uses the word most, and the other uses some. You must analyse these to decide which of the two conclusions must follow logically if the statements are true. Given Data / Assumptions: Statement I: Most crops are machines. Statement II: Some machines are fools. Conclusion I: Some fools are machines. Conclusion II: Some crops are fools. Most crops are machines implies that at least some crops are machines. Concept / Approach: The phrase some machines are fools means there is at least one element that belongs to both machines and fools. This alone is enough to derive that some fools are machines, because the overlap is symmetric. The statement most crops are machines tells us that many crops lie in the machines set, but it does not specify any direct connection between crops and fools. We need to test whether we are forced to have an overlap between crops and fools, or whether that overlap is optional. Step-by-Step Solution: Step 1: Interpret statement II. Some machines are fools means that machines ∩ fools is non empty. So there is at least one object that is both a machine and a fool. Step 2: Conclusion I, some fools are machines, is just the same overlap described from the other side. Since some machines are fools, it is equally true that some fools are machines. Step 3: Therefore conclusion I must follow from statement II alone, regardless of what statement I says. Step 4: Now interpret statement I. Most crops are machines indicates that more than half of all crops are in the machines set. At minimum, it implies that there are some crops that are machines. Step 5: To get conclusion II, some crops are fools, we would need at least one element that is both a crop and a fool. Step 6: Even though some machines are fools and many crops are machines, it is still possible that none of the machines that are crops are the same machines that are fools. The sets crops and fools can still be disjoint while both statements remain true. Verification / Alternative check: Construct a simple example. Let machines be {m1, m2, m3, m4}, crops be {m1, m2} and fools be {m3}. Then most crops (both m1 and m2) are machines, so statement I holds. Some machines (m3) are fools, so statement II also holds. However, there is no object that is both a crop and a fool, so conclusion II fails. At the same time, some fools are machines is true because m3 is both a machine and a fool, so conclusion I holds. This confirms that conclusion I is forced, but conclusion II is not. Why Other Options Are Wrong: Option B chooses only conclusion II, ignoring the direct equivalence between some machines are fools and some fools are machines. Option C says neither conclusion follows, but conclusion I must hold whenever statement II is true. Option D claims both follow, but example constructions show that crops and fools can remain disjoint. Option E suggests that exactly one of them follows without specifying, but you are expected to identify conclusion I as the specific valid conclusion. Common Pitfalls: Students often confuse most with all and think that if most crops are machines and some machines are fools, then some crops must be fools. This is not logically guaranteed because the overlapping part between machines and fools might lie entirely outside the subset of machines that are crops. Another common error is to overlook simple symmetric rephrasing, as in moving from some machines are fools to some fools are machines. Final Answer: The correct logical outcome is that only conclusion I follows from the given statements.

Statement and Conclusion Questions