1. (P $ \lor $ Q) ⊃ R
2. R ⊃ ∼Q
-Which of the following propositions is derivable from the given premises using the rules available through section 3.5 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN, Cont, Impl, Equiv, Exp, Taut)?

Question

Quizplus · Accepted Answer

From premise 2, R ⊃ ∼Q, we can use Modus Tollens (MT) to derive ∼∼Q, which is equivalent to Q. Then, from premise 1, (P ჱ Q) ⊃ R, and Q, we can use Simplification (Simp) to derive Q. Hence, the only derivable proposition is D, ∼Q.

1 (P ∨ \lor ∨ Q) ⊃ R 2

1 (P $\lor$ Q) ⊃ R
2