Logical deduction – translating "only when": Statement: "Only when it is not quiet, Reshma studies." Which two statements can both be true in a way that is consistent with the given rule? (i) It is quiet. (ii) It is not quiet. (iii) Reshma studies. (iv) Reshma does not study.
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A(ii) (iii)
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B(ii) (iv)
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C(i) (iii)
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D(iii) (i)
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ENone of these
Answer
Correct Answer: (ii) (iii)
Explanation
Introduction / Context:The sentence "Only when it is not quiet, Reshma studies" is a classic conditional of the form Studies → NotQuiet. It does not say that whenever it is not quiet she must study; it only forbids studying in quiet conditions.
Given Data / Assumptions:
- Rule: Reshma studies only when it is not quiet.
- Therefore: If Reshma studies, then it is not quiet.
- No statement is made about what happens when it is not quiet (she may or may not study).
Concept / Approach:Translate to implication: (iii) ⇒ (ii). The contrapositive is Quiet ⇒ NotStudy, i.e., (i) ⇒ (iv).
Step-by-Step Solution:
From "only when": Studies → NotQuiet.Thus (iii) implies (ii), so the pair (ii) (iii) is consistent and jointly possible.Pairs that assert studying while quiet, such as (i) (iii), contradict the rule.Verification / Alternative check:Consider truth-table style reasoning: the only forbidden combo is Quiet + Studies. All other combinations are allowed, including NotQuiet + Studies and NotQuiet + NotStudy.
Why Other Options Are Wrong:(i) (iii) conflicts with the rule (studying despite quiet). (ii) (iv) is allowed but does not "follow" from the rule; the rule does not force not studying when it is not quiet. (iii) (i) is the same conflict reordered.
Common Pitfalls:Reading "only when" as "if and only if." It is one-way, not biconditional.
Final Answer:(ii) (iii)