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.

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:

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)