Given the pair of statements: J ≡ ∼ M and (J

Question

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

Quizplus · Accepted Answer

From J ≡ ∼ M we can infer J • ∼ M and ∼ J • M. 
Substituting these two values in (J • M) ∨ ∼(M ∨ J) we get (∼ M • M) ∨ ∼(M ∨ ∼ M) = False ∨ ∼True = True. Therefore, we have both True and False in the same statement which is contradictory.