Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent.
-$ (p \rightarrow q) \vee(q \rightarrow p),(p \leftrightarrow q) $

A) Not equivalent
B) Equivalent

Question

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent.
-$ (p \rightarrow q) \vee(q \rightarrow p),(p \leftrightarrow q) $

A) Not equivalent
B) Equivalent

Quizplus · Accepted Answer

Using DeMorgan's laws or a truth table, we can determine that $ (p \rightarrow q) \vee (q \rightarrow p) $ simplifies to $ \text{TRUE} $ for all possible truth values of $ p $ and $ q $ because at least one of the implications will always be true. On the other hand, $ p \leftrightarrow q $ is only true when $ p $ and $ q $ have the same truth values. Therefore, they are not equivalent.

Use DeMorganʹs Laws or a Truth Table to Determine Whether (p→q)∨(q→p),(p↔q) (p \rightarrow q) \vee(q \rightarrow p),(p \leftrightarrow q) (p→q)∨(q→p),(p↔q)

Use DeMorganʹs Laws or a Truth Table to Determine Whether $(p \rightarrow q) \vee(q \rightarrow p),(p \leftrightarrow q)$