GATE Civil 2023 Set 1 | GA Question: 4

Question

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. 

Answer 1

If Donald Duck says, "All ducks always lie," and his statement is true, then it means that ducks, including himself, always lie. However, if all ducks always lie, then his statement must also be a lie. This creates a paradox, as his statement cannot be both true and false simultaneously. Therefore, we can conclude that his statement is false.

So, the correct statement is: "Donald Duck's statement is false."

Correct Answer: C

Answer 2

The correct answer is (D) Donald Duck's statement is false.

Here's why:

• If Donald Duck's statement "All ducks always lie" is true, then he himself is lying by making the statement. This creates a paradox.
• If Donald Duck is lying, then his statement isn't true. But because the statement claims that all ducks always lie, then Donald Duck being a duck is lying, making the statement true again. This creates another paradox.

Therefore, the only way to resolve these paradoxes and maintain logical consistency is to assume that Donald Duck's statement is false. In other words, if he claims all ducks always lie, then at least his own statement must be false, otherwise it creates a contradictory situation.