Give that p is false and q is true and proposition r is false, determine whether the propositions are true. $\urcorner\left(p \vee q\right) \wedge \left(\urcorner q \vee r \right)$
Can I get some feedback on if this is correct and if my syntax for breaking down the answer is good.
$\urcorner\left(p \vee q\right)$ = (p: false $\vee$ q: true) = true, then $\urcorner$($p \vee q$) = false.
$\left(\urcorner q \vee r \right)$ = ($\urcorner$q: false $\vee$ r: false) = true.
$\left(false \wedge true\right)$ = false, the proposition $\urcorner\left(p \vee q\right) \wedge \left(\urcorner q \vee r \right)$ is false.
Best Answer
I would simply answer by plugging in and reducing:
Given: $p = F$, $q = T$, $r = F$:
\begin{align} \neg (p \vee q) \wedge (\neg q \vee r) = &\neg (F \vee T) \wedge (\neg T \vee F) \\ \neg (F \vee T) \wedge (\neg T \vee F) = &\neg T \wedge (F \vee F) \\ =&F\wedge F \\ =& F \end{align}
So this assignment to $p$, $q$, and $r$ results in the expression evaluating to false.