The negation of the statement [(p q) (q ( r))] is :

Question

The negation of the statement $$(p \vee q) \wedge (q \vee ( \sim r))$$ is :

Accepted Answer

The negation of the statement $(p \vee q) \wedge(q \vee(\sim r))$ is

$$
\begin{aligned}
& =\sim[(p \vee q) \wedge(q \vee(\sim r))] \\
& =\sim[(p \vee q) \vee \sim(q \vee(\sim r)] \\
& =((\sim p) \wedge \sim q)) \vee((\sim q) \wedge r))
\end{aligned}
$$

Apply distribution law,

$$
\begin{aligned}
& =\sim q \wedge((\sim p) \vee r)) \\
& =((\sim p) \vee r) \wedge(\sim q)
\end{aligned}
$$

Solutions · 1