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?
Options:
(A) Humpty Dumpty always falls while having lunch
(B) Humpty Dumpty does not fall sometimes 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
Official Answer Key:
B
Step-by-Step Solution & Explanation
‘The wall sometimes breaks’ means it does not break every time, and a fall only occurs when the wall breaks. Therefore, on the occasions the wall does not break, Humpty Dumpty does not fall — i.e. he does not fall sometimes while having lunch, which is exactly statement (B). (A) over-generalises ‘sometimes breaks’ to ‘always falls’, which is not supported. (C) introduces ‘dinner’, a scenario never mentioned in the premises — no valid inference can be drawn about it. (D) commits a logical converse error (denying the antecedent) that is not implied by the original conditional statements. Hence (B) is the only valid inference.
Section 1 — Engineering Mathematics
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