Question

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

• A. $(p\wedge \sim q)\wedge \sim p$
• B. $(p\wedge \sim q)\vee \sim p$
• C. $(p\vee \sim q)\vee \sim p$
• D. None of these

Answer 1

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

$\sim [p\vee (\sim p\vee q\left)\right]\equiv \sim p\wedge \sim (\sim p\vee q)$
$\equiv \sim p\wedge (\sim (\sim p)\wedge \sim q)$
$=\sim p\wedge (p\wedge \sim q)$