$$\text { When using a truth table, the statement } \sim ( \mathrm { q } \rightarrow \mathrm { p } ) \text { is equivalent to } \mathrm { q } \wedge \sim \mathrm { p } \text {. }$$

Question

Quizplus · Accepted Answer

The statement $\sim ( q \rightarrow p )$ negates the implication $q \rightarrow p$. In logic, $q \rightarrow p$ is false only when $q$ is true and $p$ is false. Therefore, negating this implication ($\sim ( q \rightarrow p )$) results in a statement that is true when $q$ is true and $p$ is false, which is exactly when $q \wedge \sim p$ is true.