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˥(P → Q) is equivalent to

  • A.P ^ ˥Q
  • B.P ^ Q
  • C.˥P v Q
  • D.None of these

Answer: A

Correct answer: P ^ ˝Q

An implication is false in exactly one case, when the antecedent is true and the consequent false, so its negation asserts precisely that case. Formally \( \lnot(P \to Q) \equiv \lnot(\lnot P \lor Q) \equiv P \land \lnot Q \) by De Morgan. Note that the result is a conjunction, not another implication.

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