GATE CS 2026 Set 1 Q.5: Analytical and Logical Reasoning

'When the teacher is in the room, all students stand silently.'

If the above statement is true, which one of the following statements is not necessarily true?

If any student is not standing silently, then the teacher is not in the room.

When the teacher is in the room, all students are silent.

If all students are standing, then the teacher is in the room.

When the teacher is in the room, all students are standing.

Official answer and solution

Official answer: C
From: Official GATE 2026 answer key

Solution

Model the statement as an implication $T \rightarrow (S \wedge Q)$ and identify the option that commits the fallacy of affirming the consequent.

Let $T$ be 'the teacher is in the room', $S$ be 'all students are standing', and $Q$ be 'all students are silent'. The given statement is $T \rightarrow (S \wedge Q)$ .

Option (A) is the contrapositive $\neg(S \wedge Q) \rightarrow \neg T$ , which is logically equivalent to the given statement.
Option (B) ( $T \rightarrow Q$ ) and Option (D) ( $T \rightarrow S$ ) follow directly by conjunction elimination.
Option (C) claims $S \rightarrow T$ (the converse of $T \rightarrow S$ ), which is not necessarily true because students may stand even when the teacher is not in the room.

Final answer

Option (C)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 1 (CS1)
Question: 5 of 65
Section: General Aptitude

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.

Question

Solution

Source