'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 the above statement is true, which one of the following statements is not necessarily true?
Show Hint
- 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.
The Correct Option is C
Solution and Explanation
A clean way to attack this kind of question is to sort every option into one of three logical relationships with the original statement $T \rightarrow S$ (teacher present implies students stand silently): the contrapositive, always equivalent to the original; a weakened consequence, always implied by the original; or the converse, never guaranteed by the original.
Option (A) is the contrapositive, which always carries the same truth value as $T \rightarrow S$, so it is guaranteed true. Options (B) and (D) each replace "stand silently" with just one of its two components, "silent" or "standing." Since "stand silently" already forces both of these individually, both (B) and (D) are weaker statements that the original guarantees, so both are necessarily true.
Option (C), however, is the converse (students standing implies teacher present). A conditional statement never guarantees its own converse; there could easily be situations, unrelated to the teacher's presence, that also cause all students to stand. Therefore only option (C) fails to be guaranteed by the original statement, making it the answer.
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