1. A ⊃ ∼B
2. A $ \lor $ (B ≡ ∼C)
3. B
-Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?
A) ∼A
B) ∼∼B
C) (A $ \lor $ B) ≡ (A $ \lor $ ∼C)
D) Options A, B, and C
E) Options A and B, but not C

Question

Quizplus · Accepted Answer

From premise 1, A implies not B (A ⊃ ∼B), which means if A is true, B must be false. However, premise 3 states B is true, which means A must be false. Therefore, B is true, and ∼∼B (which is equivalent to B) is an immediate consequence.

1 a ⊃ ∼B 2 ∨ \lor ∨ (B ≡ ∼C) 3

1 a ⊃ ∼B
2 $\lor$ (B ≡ ∼C)
3