Given p is true, q is true, and r is false, find the truth value of the statement.
-$( \sim p \wedge q ) \rightarrow \sim r$

Question

Quizplus · Accepted Answer

The statement $( \sim p \wedge q ) \rightarrow \sim r$ simplifies as follows: Since $p$ is true, $\sim p$ (not $p$) is false. The conjunction $( \sim p \wedge q )$ is false because one of its components ($\sim p$) is false. In logic, a statement of the form $false \rightarrow true$ (or $false \rightarrow$ anything) is always true, because a false premise in a conditional statement makes the whole statement true. Since $r$ is false, $\sim r$ is true, making the conditional statement true.

Given P Is True, Q Is True, and R Is (∼p∧q)→∼r( \sim p \wedge q ) \rightarrow \sim r(∼p∧q)→∼r

Given P Is True, Q Is True, and R Is $( \sim p \wedge q ) \rightarrow \sim r$