Logical deduction – biconditional ("if and only if"): "Arya takes fries if and only if she gets it free with a cheese burger." Which pair must hold together? (i) Arya got a burger. (ii) Arya had fries. (iii) Arya got a cheese burger. (iv) Arya did.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:An "if and only if" (iff) statement creates a two-way linkage: Fries ⇔ (Free-with-cheese-burger). Either side being true forces the other true; either side being false forces the other false. Given Data / Assumptions: Fries iff Cheese-burger-free (with fries) condition. Plain "got a burger" in (i) is irrelevant unless it is a cheese burger given free with fries. Concept / Approach:From the biconditional, (ii) ↔ (iii). Thus whenever (iii) is true, (ii) is true, and vice versa. Step-by-Step Solution: (iii) ⇒ (ii) by "only if" direction (if CB-free then fries).(ii) ⇒ (iii) by "if" direction (if fries then CB-free).Therefore both pairs (iii) (ii) and (ii) (iii) are correct. Verification / Alternative check:Truth-table of p ⇔ q shows p and q always share the same truth value. Why Other Options Are Wrong:(i) (ii) does not follow; (i) says nothing about cheese or free. (iv) contradicts (ii). Common Pitfalls:Confusing "only if" (one-way) with "if and only if" (two-way). Final Answer:Both (a) and (b)

Logical deduction – biconditional ("if and only if"): "Arya takes fries if and only if she gets it free with a cheese burger." Which pair must hold together? (i) Arya got a burger. (ii) Arya had fries. (iii) Arya got a cheese burger. (iv) Arya did not have fries.

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