'When the teacher is in the room, all students stand silently.' If the above statement is true, whic

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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?

Accepted Answer

Correct Answer: (C)Concept -- Propositional Logic and Implication Converse: The given statement is: Teacher in room (T) implies All students stand silently (S). In formal logic: T → S. From T → S we can validly derive: A (Contrapositive): ¬S → ¬T. This is logically equivalent to the original (modus tollens) and therefore necessarily true. B: T → students are silent (part of 'stand silently'). This is directly implied (since 'stand silently' includes being silent). D: T → all students are standing (again part of 'stand silently'). True. C: All students standing → T. This is the converse of T → standing, which is not necessarily true. Students could all stand for other reasons (another teacher, a fire drill, a command from a student leader) without the teacher being present. In logic, an implication and its converse are not equivalent; the converse may be false even when the original is true. Option C asserts the converse of the given implication, which is a logical fallacy (affirming the consequent). Standard textbooks on logic emphasize that from P → Q, we cannot conclude Q → P.

'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?

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'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?

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More Questions from Analytical Aptitude

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