Question

select the truth value of (∼ p ∨ q) ∧ r if p is true, q is false, and r is true. select choice

Explanation:

Step1: Evaluate $\sim p$

Given $p$ is true, the negation of $p$ ($\sim p$) is false. So $\sim p = \text{False}$.

Step2: Evaluate $\sim p \vee q$

We know $\sim p = \text{False}$ and $q = \text{False}$. The disjunction ($\vee$) is true if at least one operand is true. Since both are false, $\sim p \vee q = \text{False}$.

Step3: Evaluate $(\sim p \vee q) \wedge r$

We have $(\sim p \vee q) = \text{False}$ and $r = \text{True}$. The conjunction ($\wedge$) is true only if both operands are true. Since one is false, $(\sim p \vee q) \wedge r = \text{False}$.

Answer:

False