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

Question

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

Quizplus · Accepted Answer

Both $p$ and $q$ are true statements, while $r$ is false. Thus, $\sim ( p \wedge r )$ and $\sim ( q \wedge r )$ are both true because $r$ being false makes $p \wedge r$ and $q \wedge r$ false, and their negations true.

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

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