GATE CS 2026 Set 1 — Question 5
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General Aptitude → Analytical Aptitude → Deduction & Induction
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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?
Correct answer
(C) If all students are standing, then the teacher is in the room.
Solution
Let be the proposition "The teacher is in the room" and be the proposition "All students stand silently".
The given statement is .Let's analyze the options:
(A) "If any student is not standing silently, then the teacher is not in the room." This is , which is the contrapositive of the original statement. The contrapositive is logically equivalent to the original statement, so it is necessarily true.
(B) "When the teacher is in the room, all students are silent." Since standing silently implies being silent, this follows from . Necessarily true.
(C) "If all students are standing, then the teacher is in the room." This is (assuming "standing" is the condition , or a part of it). This is the converse of the original statement. The converse is not necessarily true. Students could be standing for other reasons even if the teacher is not present.
(D) "When the teacher is in the room, all students are standing." Since standing silently implies standing, this follows from . Necessarily true.Therefore, option (C) is not necessarily true.
The given statement is .Let's analyze the options:
(A) "If any student is not standing silently, then the teacher is not in the room." This is , which is the contrapositive of the original statement. The contrapositive is logically equivalent to the original statement, so it is necessarily true.
(B) "When the teacher is in the room, all students are silent." Since standing silently implies being silent, this follows from . Necessarily true.
(C) "If all students are standing, then the teacher is in the room." This is (assuming "standing" is the condition , or a part of it). This is the converse of the original statement. The converse is not necessarily true. Students could be standing for other reasons even if the teacher is not present.
(D) "When the teacher is in the room, all students are standing." Since standing silently implies standing, this follows from . Necessarily true.Therefore, option (C) is not necessarily true.
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