1. J ⊃ (K $ \lor $ L)
2. J ≡ ∼K
3. (∼L $ \lor $ M) • (∼L $ \lor $ N)
-Consider assuming 'J' 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) K
B) K • L
C) ∼L • (M $ \lor $ N)
D) All of the above
E) None of the above

Question

Quizplus · Accepted Answer

Given the premises and assuming 'J' for conditional proof, none of the options (A, B, C) are immediate one-step consequences in propositional logic (PL). The assumption of 'J' directly leads to 'K ∨ L' from the first premise, but none of the options are directly derivable from this without additional steps.

1 J ⊃ (K ∨ \lor ∨ L) 2 J ≡ ∼K 3

1 J ⊃ (K $\lor$ L)
2 J ≡ ∼K
3