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

Question

Quizplus · Accepted Answer

E is the correct answer because it is the logical equivalent of the first premise, ∼G • (∼H • ∼I), with the order of the conjunctions rearranged. This rearrangement does not change the logical meaning, making it an immediate consequence.

1 ∼G • (∼H • ∼I) 2 ∨ \lor ∨ H) ∨ \lor ∨

1 ∼G • (∼H • ∼I)
2 $\lor$ H) $\lor$