Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these.
-$$\sim [ ( p - q ) \wedge ( q - p ) ] \rightarrow \sim ( p \leftrightarrow q )$$
A) Tautology
B) Implication
C) Self-contradiction
D) None of these

Question

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these.
-$$\sim [ ( p - q ) \wedge ( q - p ) ] \rightarrow  \sim ( p \leftrightarrow q )$$
A) Tautology
B) Implication
C) Self-contradiction
D) None of these

Quizplus · Accepted Answer

The given statement is an implication because it has the form of $A \rightarrow B$, where $A$ is the negation of $[( p \rightarrow q ) \wedge ( q \rightarrow p )]$ and $B$ is $\sim ( p \leftrightarrow q )$. The statement essentially says that if it is not the case that $p$ implies $q$ and $q$ implies $p$ simultaneously, then $p$ and $q$ do not have the same truth value. This is a conditional statement, making it an implication.

Determine Whether the Statement Is a Self-Contradiction, an Implication, a Tautology