The GATE Grind

GATE 2026 DA – Question 38

Artificial Intelligence · Logic: propositional and predicate · 2 marks · Multiple choice

Assume that a Creative ($C$) person will Succeed ($S$) if the person is also Disciplined ($D$), but will not succeed otherwise. Now, consider the following statements:

(i) $C \wedge S \Leftrightarrow D$

(ii) $C \Rightarrow (S \Leftrightarrow D)$

(iii) $C \Leftrightarrow ((D \Rightarrow S) \vee \neg S)$

Which of the following options is correct?

  1. Both (i) and (ii) are TRUE
  2. Only (ii) is TRUE
  3. Both (ii) and (iii) are TRUE
  4. Only (iii) is TRUE

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Show answer and explanation

Correct answer: (B) Only (ii) is TRUE

Explanation

The assumption says that for a creative person success happens exactly when the person is disciplined, which is $C \Rightarrow (S \Leftrightarrow D)$. That is statement (ii), so it is true. Statement (i) reads $(C \wedge S) \Leftrightarrow D$, which also constrains people who are not creative (a disciplined person who is not creative would have to satisfy $C \wedge S$), so it does not follow. In (iii), $(D \Rightarrow S) \vee \neg S = \neg D \vee S \vee \neg S$ is always true, so (iii) says $C \Leftrightarrow True$, that is $C$, which is not implied. Only (ii) is true.