Question 1

Logical deduction – visitors of the Taj are tourists or historians: Which pair aligns with "Those visiting the Taj Mahal are either tourists or historians"? (i) Siya is historian or a tourist. (ii) Riya is a tourist. (iii) Siya is visiting the Taj M…

Accepted Answer

Introduction / Context: The rule is VisitTaj ⇒ (Tourist ∨ Historian). It does not say all tourists/historians visit Taj. Given Data / Assumptions: For any person X, if X visits Taj, then X is tourist or historian. Concept / Approach: We look for a pair where visiting Taj justifies labeling the person as tourist or historian. That is (iii) then (i) for Siya. Step-by-Step Solution: From (iii) Siya visits Taj ⇒ conclude (i) Siya is historian or tourist.Statements about Riya are independent; not required by the rule. Verification / Alternative check: Implication direction is from visiting to category membership, not the reverse. Why Other Options Are Wrong: (iv) (ii) assumes visiting ⇒ tourist for Riya without (iv) being given by the rule. (i) (iii) flips order; (i) alone does not imply (iii). Common Pitfalls: Assuming all tourists/historians must be visitors (converse error). Final Answer: (iii) (i)

Question 2

Logical deduction – constraint on selection order: "When Anu comes first and Tanu comes second, Nikki and Sona cannot be selected in that order." Choose a consistent pair. (i) Anu and Tanu came first. (ii) Anu came first and Tanu came second. (iii) …

Accepted Answer

Introduction / Context: The conditional bans a specific outcome (Nikki then Sona) when a particular ranking holds (Anu 1st, Tanu 2nd). It does not forbid the reverse (Sona then Nikki). Given Data / Assumptions: If (Anu 1st ∧ Tanu 2nd) then Not(Nikki then Sona). No other orders are excluded by the rule. Concept / Approach: Pick the option that asserts the condition and a permitted selection order. (ii) states the condition, and (iv) supplies an allowed order. Step-by-Step Solution: Assume (ii) holds.The prohibited sequence is (iii). Therefore (iv) is consistent. Verification / Alternative check: Check (ii) (iii): violates the constraint, so invalid. (i) is vague and incomplete about positions. Why Other Options Are Wrong: (ii) (iii) contradicts the rule. (i) (iv) is ambiguous since (i) does not fully specify "first" and "second" respectively for Anu and Tanu. Common Pitfalls: Thinking both orders (Nikki→Sona and Sona→Nikki) are banned; only one is. Final Answer: (ii) (iv)

Question 3

Logical deduction – library visitors are only students or teachers: Determine a valid pair. (i) Rajesh is in the library. (ii) Shiva is in the library. (iii) Rajesh is a student. (iv) Shiva may be a teacher.

Accepted Answer

Introduction / Context: The statement "Only students or teacher visit the library" means InLibrary ⇒ (Student ∨ Teacher). We can draw categorization conclusions from presence in the library. Given Data / Assumptions: If a person is in the library, they must be a student or a teacher. Concept / Approach: (i) asserts presence; thus (iii) is a valid specific instantiation. (ii) (iv) is also compatible, but the question asks for a definitive pair implied by the rule; (i) (iii) is a clean consequence. Step-by-Step Solution: From (i) InLibrary(Rajesh) ⇒ Rajesh ∈ {Student,Teacher}.Choosing "student" satisfies the rule; hence (iii) follows as a permissible deduction in MCQ framing. Verification / Alternative check: We cannot deduce both category and presence in reverse; category labels alone do not imply presence. Why Other Options Are Wrong: (ii) (iv) is possible but not a strict consequence (could as well be student). (iii) (i) is reversed order (not a logical implication). Common Pitfalls: Reading "only" as "if and only if." Final Answer: (i) (iii)

Question 4

Logical deduction – "only romantic boys give roses": Which pair is a valid consequence? (i) Ashok is romantic. (ii) Ashok gave roses to a girl. (iii) Ashok did not give roses to a girl. (iv) Ashok is a romantic boy.

Accepted Answer

Introduction / Context: "Only romantic boys give roses" means GiveRoses ⇒ RomanticBoy. It does not claim that all romantic boys give roses. Given Data / Assumptions: If someone gave roses, they must be a romantic boy. Concept / Approach: (ii) implies (iv) directly by the rule. Any converse pairing is not guaranteed. Step-by-Step Solution: Assume (ii) is true.By implication, conclude (iv) is true. Verification / Alternative check: Counterexamples exist for (i) ⇒ (ii): a romantic boy may still choose not to give roses. Why Other Options Are Wrong: (i) (ii) assumes converse. (i) (iii) is consistent but not a consequence. (ii) (i) is weaker than (ii) (iv) because it omits "boy" and romantic status exactly as stated. Common Pitfalls: Confusing necessity with sufficiency. Final Answer: (ii) (iv)

Question 5

Logical deduction – simple conditional: "If you propose to the government, it will relent." Identify the valid pair. (i) Amit proposed to the government. (ii) Amit relented. (iii) Government relented. (iv) Government did not relent.

Accepted Answer

Introduction / Context: Let P = "propose to the government" and R = "government relents." The statement is P ⇒ R. Given Data / Assumptions: If P happens, R must happen. Concept / Approach: We need a pair where P co-occurs with R. (i) (iii) expresses precisely that. Step-by-Step Solution: From (i) P is true.Therefore (iii) must be true. Verification / Alternative check: Pairs involving not-relent contradict the rule if P is asserted. Why Other Options Are Wrong: (iii) (i) flips order. (iv) (ii) and (ii) (iv) are irrelevant or contradictory. Common Pitfalls: Attaching "Amit relented" to the agent; the statement concerns the government. Final Answer: (i) (iii)

Question 6

Logical deduction – "all that flows have viscosity": Choose the correct implication or contrapositive pair. (i) It flows. (ii) It does not flow. (iii) It has viscosity. (iv) It does not have viscosity.

Accepted Answer

Introduction / Context: "All that flows have viscosity" is Flows ⇒ HasViscosity. The logically equivalent contrapositive is NotHasViscosity ⇒ NotFlows. Given Data / Assumptions: If something flows, it must have viscosity. If it lacks viscosity, it cannot flow. Concept / Approach: Option (iv) (ii) states the contrapositive pair: not having viscosity implies not flowing. Step-by-Step Solution: Flows ⇒ HasViscosity.Contrapositive: NotHasViscosity ⇒ NotFlows.Thus (iv) (ii) is valid. Verification / Alternative check: (iii) (i) incorrectly assumes HasViscosity ⇒ Flows (converse). Many solids have viscosity-defined properties but do not "flow" macroscopically. Why Other Options Are Wrong: (iii) (i) is converse fallacy. (c) is meaningless as written. (d) is false. Common Pitfalls: Reversing subset implications. Final Answer: (iv) (ii)

Question 7

Logical deduction – Sunday implies Tuesday: "If it happens on Sunday, it will happen again on Tuesday." Choose the consistent pair. (i) It happened on Sunday. (ii) It happened on Tuesday. (iii) It did not happen on Sunday. (iv) It did not happen on …

Accepted Answer

Introduction / Context: The rule is Sunday ⇒ Tuesday. Thus whenever Sunday occurs, Tuesday must also occur. The converse need not hold. Given Data / Assumptions: If (i) is true, (ii) must be true. Concept / Approach: A consistent pair containing both truths is fine; the order listed in the option does not affect logical consistency. Step-by-Step Solution: Assume Sunday occurred.By the rule, conclude Tuesday occurred too. Verification / Alternative check: Pairs involving "did not happen on Tuesday" with "happened on Sunday" would contradict the rule. Why Other Options Are Wrong: (iii) (ii) and (iii) (iv) start by denying Sunday; they tell nothing decisive about Tuesday. The chosen pair affirms both, which is fully consistent with the rule. Common Pitfalls: Expecting a biconditional; it is only one-way necessity. Final Answer: (ii) (i)

Question 8

Logical deduction – "whenever Shashi makes coffee, Asha puts in sugar": Pick the valid consequence. (i) Shashi makes coffee. (ii) Asha makes coffee. (iii) Shashi puts in sugar. (iv) Asha puts in sugar.

Accepted Answer

Introduction / Context: The rule is MakeCoffee(Shashi) ⇒ PutsSugar(Asha). It does not say who makes coffee other times, nor that Shashi puts sugar. Given Data / Assumptions: Trigger: Shashi makes coffee. Effect: Asha puts sugar. Concept / Approach: We need a pair that states the antecedent and its direct consequence: (i) then (iv). Step-by-Step Solution: From (i), apply implication.Conclude (iv). Verification / Alternative check: Statements (ii) and (iii) are irrelevant or incorrect ties to the rule. Why Other Options Are Wrong: (iv) (i) flips order. (ii) (iii) and (iii) (ii) are not implied by the rule. Common Pitfalls: Assuming Shashi is the one adding sugar. Final Answer: (i) (iv)

Question 9

Logical deduction – Batman enters ⇒ Superman exits: "Superman exits from the window, when Batman enters from the door." Choose the valid pair. (i) Superman exits from the window. (ii) Batman enters from the door. (iii) Superman does not exit from th…

Accepted Answer

Introduction / Context: The structure is BatmanEnters ⇒ SupermanExits. So whenever (ii) holds, (i) must also hold. Given Data / Assumptions: No converse is stated. Concept / Approach: Pick the pair that asserts both the antecedent and the necessary consequent: (ii) and (i). The option lists them as (i) (ii), which is still the same pair of truths. Step-by-Step Solution: Assume (ii) true.Deduce (i) true. Verification / Alternative check: Pairs (iii) (iv) or (iv) (iii) jointly negate both and are not consequences. Why Other Options Are Wrong: They neither reflect the implication nor provide a necessary connection. Common Pitfalls: Interpreting the wording as biconditional. Final Answer: (i) (ii)

Question 10

Logical deduction – "Anu drinks tea only when Dolly eats samosa": Select the correct pair. (i) Dolly ate samosa. (ii) Anu drank tea. (iii) Anu did not drink tea. (iv) Dolly did not eat samosa.

Accepted Answer

Introduction / Context: "Only when" again signals a one-way necessity: Tea(Anu) ⇒ AteSamosa(Dolly). It does not guarantee that Dolly eating samosa makes Anu drink tea. Given Data / Assumptions: If Anu drank tea, Dolly must have eaten samosa. Concept / Approach: Thus the pair (ii) (i) is the implication with its necessary condition. Step-by-Step Solution: Assume (ii) is true.Conclude (i) is true by the rule. Verification / Alternative check: (i) (ii) would be an unstated converse; (ii) (iv) contradicts the rule. Why Other Options Are Wrong: (iii) (ii) is self-contradictory. Common Pitfalls: Mistaking necessary for sufficient conditions. Final Answer: (ii) (i)

Question 11

Logical deduction – "clouds go high ⇒ hail": Find the valid consequence. (i) Clouds went high. (ii) It is raining hail. (iii) Clouds went low. (iv) It is not raining hail.

Accepted Answer

Introduction / Context: This is a direct conditional: HighClouds ⇒ Hail. We match antecedent with its consequent. Given Data / Assumptions: (i) being true forces (ii) to be true. Concept / Approach: Select the pair that shows both occurring together: (i) (ii). Step-by-Step Solution: Assume (i): clouds went high.Then (ii): raining hail must be true. Verification / Alternative check: Other statements either contradict or are irrelevant to the stated implication. Why Other Options Are Wrong: They either reverse or negate without support. Common Pitfalls: Expecting biconditional behavior. Final Answer: (i) (ii)

Question 12

Logical deduction – "mango rots when it is ripe": Choose the correct consistent pair. (i) Mango is ripe. (ii) Mango is not ripe. (iii) Mango rots. (iv) Mango does not rot.

Accepted Answer

Introduction / Context: "When ripe, it rots" gives Ripe ⇒ Rot. The contrapositive is NotRot ⇒ NotRipe. We seek a pair that can co-occur under the rule. Given Data / Assumptions: Ripe implies Rot. Concept / Approach: Both "rots" and "ripe" can be true together; the option lists them as (iii) (i). Step-by-Step Solution: Assume (i) is true ⇒ (iii) must be true.Thus the pair (iii) (i) is consistent. Verification / Alternative check: (ii) (iv) is also consistent by contrapositive, but the key consequence directly linked in the rule is from ripeness to rotting; the offered correct pair captures that co-truth. Why Other Options Are Wrong: (ii) (iii) is incompatible (not ripe yet rotting under the given rule). Common Pitfalls: Assuming Rot ⇒ Ripe (converse), which is not entailed. Final Answer: (iii) (i)

Question 13

Logical deduction – "only the hardy can climb Sagarmatha": Pick the valid implication. (i) Santosh climbed Sagarmatha. (ii) Santosh did not climb Sagarmatha. (iii) Santosh is hardy. (iv) Santosh may be hardy.

Accepted Answer

Introduction / Context: "Only the hardy can climb" means Climb ⇒ Hardy. It does not say Hardy ⇒ Climb. Given Data / Assumptions: From a successful climb, infer hardiness. Concept / Approach: (i) implies (iii); hence choose (i) (iii). Step-by-Step Solution: Assume Santosh climbed.Conclude Santosh is hardy. Verification / Alternative check: (iii) (i) is the converse and not guaranteed. Why Other Options Are Wrong: They either assert converse or provide unrelated negations/possibilities. Common Pitfalls: Reading "only" as biconditional. Final Answer: (i) (iii)

Question 14

Logical deduction – Red Riding Hood and the Big Bad Wolf: "When Red Riding Hood comes, the Big Bad Wolf is not far behind." Choose the correct pair. (i) Big Bad Wolf is behind. (ii) Red Riding Hood comes. (iii) Big Bad Wolf is not far behind. (iv) R…

Accepted Answer

Introduction / Context: The implication is RRHComes ⇒ WolfNotFarBehind. We need a pair reflecting that co-occurrence. Given Data / Assumptions: If RRH appears, the wolf is close behind. Concept / Approach: Select (ii) with (iii), aligning antecedent and consequent. Step-by-Step Solution: Assume (ii) true.Then (iii) must be true. Verification / Alternative check: (ii) (i) is weaker and uses a different predicate ("behind" vs "not far behind"). Why Other Options Are Wrong: They either contradict or fail to capture the stated consequence. Common Pitfalls: Overlooking the "not far" qualifier. Final Answer: (ii) (iii)

Question 15

Logical deduction – "all mountaineers climb": Determine the valid implication involving Amit. (i) Amit is a mountaineer. (ii) Amit is not a mountaineer. (iii) Amit climbed. (iv) Amit did not climb.

Accepted Answer

Introduction / Context: The universal statement is Mountaineer ⇒ Climbs. So for any named individual, if they are a mountaineer, we can infer that they climb. Given Data / Assumptions: (i) being true forces (iii) to be true. Concept / Approach: Pick the pair that states the antecedent category followed by the necessary action: (i) (iii). Step-by-Step Solution: Assume Amit is a mountaineer.By rule, Amit climbed. Verification / Alternative check: (iii) (i) is converse; climbing alone does not prove mountaineer status. Why Other Options Are Wrong: (ii) (iv) asserts a separate possibility but is not a consequence of the universal statement. Common Pitfalls: Conflating subset and superset relationships. Final Answer: (i) (iii)

Question 16

Logical deduction with biconditional (↔): Statement: “If and only if it is July, it will rain.” Consider the four simple statements: (i) It rains. (ii) It does not rain. (iii) It is July. (iv) It is not July. Which option lists a pair of statements …

Accepted Answer

Introduction / Context: Biconditional reasoning (“if and only if”) links two propositions so that each is both necessary and sufficient for the other. Here, the sentence “If and only if it is July, it will rain” asserts an exact pairing between the month being July and rain occurring. We must determine which pair of simple statements can be true at the same time without contradicting this biconditional. Given Data / Assumptions: Let J represent “It is July.” Let R represent “It rains.” The given statement is J ↔ R (J if and only if R). Simple statements listed are: (i) R, (ii) not R, (iii) J, (iv) not J. Concept / Approach: For a biconditional J ↔ R, the truth table has two satisfying rows: both true (J = true, R = true) or both false (J = false, R = false). Mixed cases (J true and R false, or J false and R true) violate the biconditional. Therefore, the only compatible pairs among the options are the ones where J and R have the same truth value. Step-by-Step Solution: 1) Translate: “If and only if it is July, it will rain” → J ↔ R.2) Biconditional satisfaction requires: either (J and R) or (not J and not R).3) Inspect options:• (i) (ii): R and not R → contradiction; impossible.• (iii) (ii): J and not R → violates J ↔ R.• (ii) (iii): same as above, just swapped order.• (i) (iii): R and J → matches the “both true” satisfying case. Verification / Alternative check: If there were an option listing (ii) (iv) (i.e., not R and not J), that would also be valid. Since it does not appear, the only correct pair provided is (i) with (iii). Why Other Options Are Wrong: (i) (ii): Contradictory—cannot both rain and not rain. (iii) (ii) / (ii) (iii): These encode J and not R, which contradicts J ↔ R. None of these: Not appropriate because (i) (iii) is valid. Common Pitfalls: Reading “if and only if” as a one-way implication; it is a two-way link. Assuming “if July then rain” but allowing “rain without July.” The biconditional forbids that. Final Answer: (i) (iii)

Logical Deduction Questions