Let P and Q be two propositions, ¬ (P ↔ Q) is equivalent to : (I) P ↔ ¬ Q (II)…
2017
Let P and Q be two propositions, ¬ (P ↔ Q) is equivalent to :
(I) P ↔ ¬ Q (II) ¬ P ↔ Q (III) ¬ P ↔ ¬ Q (IV) Q → P
- A.
Only (I) and (II)
- B.
Only II and III
- C.
Only III and IV
- D.
None of the above
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Correct answer: A
A biconditional P ↔ Q is true when P and Q have the same truth value. Therefore ¬(P ↔ Q) is true when P and Q have opposite truth values. Statement I, P ↔ ¬Q, is true exactly when P and Q are opposite. Statement II, ¬P ↔ Q, also expresses the same condition. Statement III is equivalent to P ↔ Q, and statement IV is not equivalent to the exclusive-or condition. Hence only statements I and II are correct.
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