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

Question

Quizplus · Accepted Answer

C) H • K is an immediate consequence because it directly follows from premise 3 (K • H) by the commutativity of conjunction, which allows us to switch the order of the conjuncts without changing the meaning.

1 G ⊃ ∼(H ∨ \lor ∨ I) 2 J ∨ \lor ∨

1 G ⊃ ∼(H $\lor$ I)
2 J $\lor$