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

Question

Quizplus · Accepted Answer

From premise 4, we have ∼∼F, which simplifies to F. Given premise 3, ∼F $ \lor $ E, and knowing F is true, the only way for the disjunction to hold is if E is true. This is because a disjunction (∼F $ \lor $ E) is true if at least one of its components is true. Since we know ∼F is false (because F is true), E must be true.

1 (A ⊃ B) • (C ⊃ D) 2 ∨ \lor ∨

1 (A ⊃ B) • (C ⊃ D)
2 $\lor$