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(P v Q) ^ (P → R )^ (Q →S) is equivalent to

  • A.S ^ R
  • B.S → R
  • C.S v R
  • D.All of above

Answer: C

Correct answer: S v R

This is the constructive dilemma. \( P \lor Q \) guarantees that at least one of P and Q holds; if P holds then \( P \to R \) gives R, and if Q holds then \( Q \to S \) gives S. Either way at least one of R and S is true, which is exactly \( S \lor R \). Nothing stronger follows, since neither R nor S is guaranteed on its own.

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