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.

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:

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)