GATE 2026 DA Q.38: solution and answer

GATE 2026 · DAQ.38 · 2 marks · MCQ

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) $C \land S \Leftrightarrow D$
(ii) $C \Rightarrow (S \Leftrightarrow D)$
(iii) $C \Leftrightarrow ((D \Rightarrow S) \lor \neg S)$

Which of the following options is correct?

(A)
Both (i) and (ii) are TRUE
(B)
Only (ii) is TRUE
(C)
Both (ii) and (iii) are TRUE
(D)
Only (iii) is TRUE

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Answer and solution

ANSWER

Option (B): only statement (ii) is TRUE.

Official answer: BSource: Official answer key, GATE 2026 DA (IIT Guwahati)

The assumption says: a creative person succeeds if disciplined and does not succeed otherwise. So whenever $C$ holds, $S$ and $D$ have the same truth value: $C \Rightarrow (S \Leftrightarrow D)$ . This is exactly statement (ii), so (ii) is TRUE.
Statement (i), with $\land$ binding tighter than $\Leftrightarrow$ , reads $(C \land S) \Leftrightarrow D$ . The assumption says nothing about a person who is not creative, so $D$ can be true while $C$ is false.
Counter-case for (i): take $C = F$ , $D = T$ , and any $S$ . The assumption still holds, because $C \Rightarrow (S \Leftrightarrow D)$ is vacuously true when $C$ is false. But $C \land S$ is F and $D$ is T, so $(C \land S) \Leftrightarrow D$ is F. Statement (i) is therefore not guaranteed, so it is FALSE.
Simplify the right side of (iii): $(D \Rightarrow S) \lor \neg S = \neg D \lor S \lor \neg S$ , which is a tautology (T) because $S \lor \neg S$ is always true.
So (iii) becomes $C \Leftrightarrow T$ , which is just $C$ . The assumption does not force $C$ to be true: with $C = F$ the assumption holds but (iii) is FALSE. So (iii) is not guaranteed, so it is FALSE.
Only (ii) is TRUE, which is option (B).

KEY IDEA

A statement of the form "if X then (S iff D)" is a conditional. It says nothing when the condition $C$ is false, so any statement that must hold for non-creative people as well is not guaranteed.

WATCH OUT FOR

Reading the assumption as a full biconditional between $D$ and success for everyone, and so accepting (i). The assumption applies only to creative people, so $C = F$ , $D = T$ breaks (i). Another slip is missing that the right side of (iii) is a tautology, which turns (iii) into plain $C$ .

From the GATE 2026 DA paper. Every question of this paper · Download the full paper · All 7 Logic questions, with notes

GATE 2026 DA Q.38: solution and answer

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