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

A) Equivalent
B) Not equivalent

Question

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

A) Equivalent
B) Not equivalent

Quizplus · Accepted Answer

Both expressions are equivalent because they both essentially state that $p$ and $q$ must have the same truth value for the overall statement to be true. DeMorgan's laws help in transforming logical expressions, but in this case, analyzing the expressions directly or using a truth table shows that both $ (q \rightarrow p) \wedge (p \rightarrow q) $ and $ q \leftrightarrow p $ are true only when $p$ and $q$ are both true or both false, making them equivalent.

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

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