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

Question

Quizplus · Accepted Answer

D) C • A is an immediate consequence because it is the commutation of premise 3 (A • C), which means the order of the conjunction does not affect its truth value.

1 a ⊃ B 2 ∨ \lor ∨ B C) (B ∨ \lor ∨

1 a ⊃ B
2 $\lor$ B
C) (B $\lor$