1. ∼(N $ \lor $ O)
2. P ⊃ ∼Q
-Consider assuming 'N $ \lor $ P' for conditional proof. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises with that further assumption for conditional proof?
A) ∼N $ \lor $ ∼O
B) ∼N • ∼O
C) ∼N
D) ∼Q ⊃ P
E) O $ \lor $ Q

Question

Quizplus · Accepted Answer

Given the premises and the assumption for conditional proof, the immediate one-step consequence is B) ∼N • ∼O. This follows from the first premise ∼(N $ \lor $ O), which by De Morgan's laws directly translates to ∼N • ∼O.

1 ∼(N ∨ \lor ∨ O) 2 P ⊃ ∼Q -Consider Assuming 'N

1 ∼(N $\lor$ O)
2 P ⊃ ∼Q
-Consider Assuming 'N