Given the pair of statements: ∼ (R ≡ M) and M

Question

Given the pair of statements: ∼ (R ≡ M) and M • ∼ R
These statements are:
A) Inconsistent.
B) Invalid.
C) Logically equivalent.
D) Consistent.
E) Contradictory.

Quizplus · Accepted Answer

If we use the truth table for the equivalence (≡) operator, we can find that ∼(R ≡ M) is equivalent to (R ∧ ∼M) ∨ (∼R ∧ M). Similarly, M • ∼R means (M ∧ ∼R) is true. Now, if we combine these two statements, we find that (R ∧ ∼M) ∨ (∼R ∧ M) and (M ∧ ∼R) are both true, which is consistent. Therefore, the correct answer is D.