GATE CS 2026 Set 1 Q5 — General Aptitude

Let us analyze the given statement using propositional logic:

Let $T$ represent: "The teacher is in the room".
Let $S$ represent: "All students stand silently" (which means they are both standing and silent).

The given statement is: $T \implies S$

Now, let us evaluate each option:

• Option A: "If any student is not standing silently, then the teacher is not in the room."
  "Any student is not standing silently" is the negation of $S$ (i.e., $\neg S$). Thus, this statement is $\neg S \implies \neg T$, which is the contrapositive of $T \implies S$. Since a conditional statement and its contrapositive are logically equivalent, this must be true.
• Option B: "When the teacher is in the room, all students are silent."
  Since $T \implies S$ (standing and silent), it logically guarantees that the students are silent when the teacher is in the room. Thus, this must be true.
• Option C: "If all students are standing, then the teacher is in the room."
  This is a form of the converse ($S \implies T$). The converse of a conditional statement is not logically equivalent to the original statement. Students could be standing for other reasons even if the teacher is not in the room. Hence, this is not necessarily true.
• Option D: "When the teacher is in the room, all students are standing."
  Since $T \implies S$ (standing and silent), it logically guarantees that the students are standing when the teacher is in the room. Thus, this must be true.