Question

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

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

Answer 1

Answer: (B)

$(p\wedge \sim q)\vee \sim p$

The negation of the compound proposition $p\wedge (\sim p\vee q)$ is,
$\equiv \sim (p\wedge (\sim p\vee q\left)\right)\equiv \sim p\vee \sim (\sim p\vee q)$
$\equiv \sim p\vee (p\wedge \sim q)\equiv (p\wedge \sim q)\vee \sim p$