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Which of the following are tautologies?

  • A.((P v Q) ^ Q) ↔ Q
  • B.((P v Q) ^ ˥P) → Q
  • C.((P v Q) ^ P) → Q
  • D.Both (a) & (b)

Answer: D

Correct answer: Both (a) & (b)

The first is the absorption law: \( (P \lor Q) \land Q \) simplifies to Q, so the biconditional is \( Q \leftrightarrow Q \) and is always true. The second is the disjunctive syllogism: given \( P \lor Q \) and \( \lnot P \), Q must hold. The third fails when P is true and Q false, since the antecedent is then true and the consequent false.

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