$$\text { Let } p \text { represent } 7

Question

$$\text { Let } p \text { represent } 7 < 8 \text {, } q \text { represent } 2 < 5 < 6 \text {, and } \mathbf { r } \text { represent } 3 < 2 \text {. Decide whether the statement is true or false. }$$
-$( \sim p \wedge q ) \vee \sim r$

Quizplus · Accepted Answer

The statement $p$ is true because $7 < 8$, $q$ is true because $2 < 5 < 6$, and $r$ is false because $3$ is not less than $2$. Thus, $\sim p$ (not $p$) is false, $q$ is true, and $\sim r$ (not $r$) is true. The expression $(\sim p \wedge q)$ is false because $\sim p$ is false and $q$ is true, making the whole conjunction false. However, $\sim r$ is true, making the entire expression $(\sim p \wedge q) \vee \sim r$ true because of the disjunction with $\sim r$.

- (∼p∧q)∨∼r( \sim p \wedge q ) \vee \sim r(∼p∧q)∨∼r

- $( \sim p \wedge q ) \vee \sim r$