‘When the teacher is in the room, all students stand silently.’ If the above…
2026
‘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. If all students are standing, then the teacher is in the room. — Let T mean “the teacher is in the room” and S mean “all students stand silently.” The given statement says T → S. From this, we can conclude S whenever T is…
- 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.
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Correct answer: C
Let T mean “the teacher is in the room” and S mean “all students stand silently.” The given statement says T → S. From this, we can conclude S whenever T is true, and we can also conclude the contrapositive ¬S → ¬T. However, the converse S → T is not necessarily true. Students may all be standing even when the teacher is not in the room. Therefore, the statement “If all students are standing, then the teacher is in the room” is not necessarily true.
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