A duck named Donald Duck says 'All ducks always lie.' Based only on the information above, which one of the following statements can be logically inferred with certainty? A. Donald Duck always lies. B. Donald Duck always tells the truth. C. Donald Duck's statement is true. D. Donald Duck's statement is false.

GATE 2023 · General Aptitude · Statements Follow · medium

Answer: D. Donald Duck's statement is false.

1. Assume Donald's statement is true: Assume 'All ducks always lie' is TRUE. Donald Duck is a duck. Therefore Donald Duck always lies. But if Donald always lies, then every statement Donald makes is a lie. Donald just stated 'All ducks always lie' — that statement must therefore be a lie, meaning it is FALSE.
2. Conclude the statement is false: Assuming the statement is true leads to a contradiction (it must then be false). By reductio ad absurdum, the assumption fails. Therefore the statement 'All ducks always lie' is FALSE.
3. Evaluate each option: Option A (Donald always lies): The false statement only tells us not every duck always lies; it does not force Donald to always lie — NOT certain. Option B (Donald always tells truth): Similarly, we cannot confirm this — NOT certain. Option C (statement is true): Ruled out in Step 1. Option D (statement is false): Proven in Step 2 — CERTAIN.