The GATE Grind

GATE 2026 DA – Question 14

Artificial Intelligence · Logic: propositional and predicate · 1 mark · Multiple choice

Which of the following statements is NOT true?

(The names of the predicates are intuitive.)

  1. $\forall x\ \forall y\ Classmate(x, y) \Rightarrow Classmate(y, x)$
  2. $\forall x\ Likes(x, Icecream) \Rightarrow \neg\exists x\ \neg Likes(x, Icecream)$
  3. “Each king is a person” is equivalent to $\forall x\ IsKing(x) \wedge IsPerson(x)$
  4. “All humans are mortal” is equivalent to $\forall x\ IsHuman(x) \Rightarrow IsMortal(x)$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) “Each king is a person” is equivalent to $\forall x\ IsKing(x) \wedge IsPerson(x)$

Explanation

A statement of the form “every $A$ is a $B$” is written with an implication, $\forall x\ (A(x) \Rightarrow B(x))$, as in option D. Option C uses a conjunction, which would say that everything in the world is both a king and a person, so it is not equivalent. Option A states that being a classmate is symmetric, which is true of classmates, and option B is the rule $\forall x\ P(x) \equiv \neg\exists x\ \neg P(x)$.