Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement.
-$[ ( \sim p \wedge \sim q ) \vee \sim q ]$

Question

Quizplus · Accepted Answer

The given compound statement simplifies as follows: Since $p$ is true, $\sim p$ (not $p$) is false. Since $q$ is false, $\sim q$ (not $q$) is true. Therefore, $(\sim p \wedge \sim q)$ simplifies to $(\text{false} \wedge \text{true})$, which is false. However, the compound statement also includes $\sim q$ (which is true) as part of an OR operation $(\vee)$. Since an OR operation is true if at least one of the components is true, the entire compound statement $[(\sim p \wedge \sim q) \vee \sim q]$ is true because $\sim q$ is true.

Let P Represent a True Statement and Let Q Represent [(∼p∧∼q)∨∼q][ ( \sim p \wedge \sim q ) \vee \sim q ][(∼p∧∼q)∨∼q]

Let P Represent a True Statement and Let Q Represent $[ ( \sim p \wedge \sim q ) \vee \sim q ]$