1. (E $ \lor $ F) ⊃ (G • H)
2. ∼E ⊃ (D ⊃ ∼D)
3. ∼G $ \lor $ ∼H
-Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?
A) (E • D) ⊃ ∼D
B) (E $ \lor $ D) ⊃ ∼D
C) E $ \lor $ (D ⊃ ∼D)
D) ∼(G • H)
E) ∼G • ∼H

Question

Quizplus · Accepted Answer

From premises 1 and 3, we can use Modus Tollens to infer ~G v ~H (~G • ~H). 
Then, using De Morgan's Law and Double Negation, we can infer ∼(G • H). Therefore, option D is an immediate consequence of the given premises.

1 (E ∨ \lor ∨ F) ⊃ (G • H) 2 ∨ \lor ∨

1 (E $\lor$ F) ⊃ (G • H)
2 $\lor$