Question 1

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 2

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 3

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 4

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 5

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 6

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 7

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 8

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 9

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