Question

‘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?

• A. If any student is not standing silently, then the teacher is not in the room.
• B. When the teacher is in the room, all students are silent.
• C. If all students are standing, then the teacher is in the room.
• D. When the teacher is in the room, all students are standing.

Hint:

A conditional statement never implies its converse. "Teacher present → students standing silently" does not mean "students standing → teacher present."

Answer 1

The Correct Option is C

Alternate approach - test with a counter-scenario: Let \(p\) = "teacher is in the room" and \(q\) = "all students stand silently." The premise \(p \rightarrow q\) is automatically true whenever \(p\) is false, regardless of \(q\).
Imagine the teacher is NOT in the room (\(p\) false), but students happen to be standing anyway for some unrelated reason (say, a fire alarm). Here \(p \rightarrow q\) still holds (since \(p\) is false), yet "all students standing" clearly did not require the teacher's presence.
This directly breaks the claim in Option C, \(\text{standing} \rightarrow p\), which is just the logical converse of the premise and is never guaranteed by it.
Options A (contrapositive), B and D (weaker consequences of \(q\)) all remain necessarily true, but Option C does not. So the statement that is NOT necessarily true is \(\text{Option C}\).