Solve the problem.
-Given that $( p \wedge q ) \vee \sim q$ is false, what can you conclude about the truth values of $p$ and $q$ ?
A) $p$ is false and $q$ is true
B) $p$ is false, $q$ can be either true or false
C) At least one of $p$ and $q$ is true
D) $p$ and $q$ can have any truth values

Question

Quizplus · Accepted Answer

For $( p \wedge q ) \vee \sim q$ to be false, both $ p \wedge q $ and $ \sim q $ must be false. $ p \wedge q $ is false if either $p$ is false or $q$ is false (or both). $ \sim q $ is false only if $q$ is true. Therefore, for the entire expression to be false, $p$ must be false and $q$ must be true.

Solve the Problem (p∧q)∨∼q( p \wedge q ) \vee \sim q(p∧q)∨∼q

Solve the Problem $( p \wedge q ) \vee \sim q$