Logical deduction – "only if" sleep condition: "Arjun falls asleep only if it is a soft bed." Which pair is consistent/consequential? (i) Arjun fell asleep. (ii) Arjun remains awake. (iii) It was a soft bed. (iv) It was a hard bed.

Introduction / Context:"Only if soft bed" translates to Sleep ⇒ SoftBed. Its contrapositive is HardBed ⇒ NotSleep (i.e., remain awake). The converse (SoftBed ⇒ Sleep) is not guaranteed.

Given Data / Assumptions:

• Rule: If Arjun fell asleep then the bed was soft.
• If the bed was hard, he could not have slept.

Concept / Approach:Look for pairs that respect Sleep ⇒ Soft and Hard ⇒ Awake. Pair (ii) (iv) asserts awake and hard bed, which aligns with the contrapositive.

Step-by-Step Solution:

Verification / Alternative check:(i) together with (iii) would also be consistent, but that exact pairing is not offered; (iii) (ii) and (ii) (iii) invert cause/effect without necessity.

Why Other Options Are Wrong:(i) (ii) is contradictory. (ii) (iii) and (iii) (ii) have no necessary link from (iii) to (ii).

Common Pitfalls:Assuming Soft ⇒ Sleep. The rule is one-way.

Final Answer:(ii) (iv)