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.
-
A(ii) (iv)
-
B(ii) (iii)
-
C(iii) (ii)
-
D(i) (ii)
-
ENone of these
Answer
Correct Answer: (ii) (iv)
Explanation
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:
From "only if": Sleep → Soft.Contrapositive: Hard → NotSleep (Awake).Thus (ii) (iv) is a valid, consistent pair.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)