1. (P $ \lor $ Q) ⊃ R
2. R ⊃ ∼Q
-Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?
A) ∼Q ⊃ R
B) R $ \lor $ ∼Q
C) ∼[∼(P $ \lor $ Q) ⊃ R]
D) ∼(P $ \lor $ Q) $ \lor $ R
E) R ⊃ (P $ \lor $ Q)

Question

Quizplus · Accepted Answer

The proposition ∼(P $ \lor $ Q) $ \lor $ R is an immediate consequence because it is logically equivalent to (P $ \lor $ Q) ⊃ R by the definition of material implication.

1 (P ∨ \lor ∨ Q) ⊃ R 2 ∨ \lor ∨

1 (P $\lor$ Q) ⊃ R
2 $\lor$