Discussion

‘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?

Answer: C

The statement that is not necessarily true is If all students are standing, then the teacher is in the room.

The given statement has the form: teacher in room implies all students stand silently.

Its contrapositive, 'if any student is not standing silently, the teacher is not in the room', is logically equivalent to it, so it must be true.
'All students are silent' and 'all students are standing' are each part of 'stand silently', so they follow whenever the teacher is in the room.
'If all students are standing, then the teacher is in the room' is the converse. The students could be standing for some other reason while the teacher is away, so it does not follow.

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