Question

The negation of the compound proposition $p\vee (\sim p\vee q)$ is

• A. $(p\wedge \sim q)\wedge \sim p$
• B. $(p\wedge \sim p)\vee \sim q$
• C. $(p\wedge \sim q)\vee \sim p$
• D. $(p\wedge \sim q)\wedge \sim q$

Answer 1

The correct option is A $(p\wedge \sim q)\wedge \sim p$

Negation of $p\vee (\sim p\vee q)$ is
$\sim [p\vee (\sim p\vee q)]=\sim p\wedge \sim (\sim p\vee q)=\sim p\wedge (\sim (\sim p)\wedge \sim q)=\sim p\wedge (p\wedge \sim q)$