Humpty Dumpty sits on a wall every day while having lunch. The wall sometimes breaks. A person sitting on the wall falls if the wall breaks. Which one of the statements below is logically valid and can be inferred from the above sentences? A. Humpty Dumpty always falls while having lunch B. Humpty Dumpty sometimes never falls while having lunch C. Humpty Dumpty never falls during dinner D. When Humpty Dumpty does not sit on the wall, the wall does not break

GATE 2015 · General Aptitude · Statements Follow · medium

Answer: B. Humpty Dumpty sometimes never falls while having lunch

1. Analyse the scenario when wall breaks: On days when the wall breaks: SittingOnWall(Humpty) AND WallBreaks => Falls(Humpty). So Humpty falls on those days.
2. Analyse the scenario when wall does NOT break: When wall does NOT break, the antecedent of Premise 3 is false, so we CANNOT conclude Humpty falls. Humpty is still on the wall but does not fall.
3. Evaluate each option: A: 'Always falls' - FALSE, wall only sometimes breaks so Humpty does not always fall. B: 'Sometimes never falls during lunch' - TRUE, on days when wall does not break, Humpty sits on intact wall and does not fall. C: 'Never falls during dinner' - Not inferable; dinner is unspecified. D: 'Wall does not break when Humpty is not sitting' - Cannot infer this, it is the fallacy of denying the antecedent.