Question

If $p \rightarrow (p \land \sim q)$ is false, then the truth values of $p$ and $q$ are, respectively

• A. T, F
• B. T, T
• C. F, F
• D. F, T

Answer 1

Answer: (B)

T, T

Answer 2

For an implication $p \rightarrow (p \land \sim q)$ to be false, the antecedent $p$ must be true, and the consequent $p \land \sim q$ must be false. Given that $p$ is true, the result $p \land \sim q$ is false only when $\sim q$ is false, which implies that $q$ is true.

Thus, the truth values are:

$p = \text{True}$ and $q = \text{True}$.