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

Question

Quizplus · Accepted Answer

Applying Modus Tollens to premises 2 and 3 yields ∼O ⊃ M and ∼O ⊃ N, respectively. Combining these two statements using conjunction yields (∼O ⊃ M) • (∼O ⊃ N), which is logically equivalent to (M ⊃ ∼N) • (∼N ⊃ M).

1 M ≡ ∼N 2 ∨ \lor ∨ (M • ∼N) D) ∼M ≡ ∼N E) N ≡

1 M ≡ ∼N
2 $\lor$ (M • ∼N)
D) ∼M ≡ ∼N
E) N ≡