1. M ≡ ∼N
2. ∼M ⊃ O
3. ∼N ⊃ O
-Which of the following propositions is derivable from the given premises using any of the twenty-five rules of PL?
A) M
B) ∼M
C) N
D) O
E) P

Question

Quizplus · Accepted Answer

From premise 1, we know that M is equivalent to the negation of N. From premises 2 and 3, we know that if either M or N are false (negated), then O must be true. Combining these statements, we can conclude that if M is false (i.e. N is true), then O must be true, since ∼N ≡ M. Similarly, if N is false (i.e. M is true), then O must also be true. Therefore, O is derivable from the given premises.