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. $(p \wedge \sim q) \sim p$
• D. none of these

Answer 1

Answer: (A)

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

Answer 2

$\sim [ P \vee ( \sim p \vee q)] \equiv\sim p \land \sim(\sim p \vee q)$ $\equiv$ $\sim p \wedge ( \sim ( \sim p) \wedge \sim q)$ $\equiv$ $\sim p \wedge (p\wedge \sim q)$ Thus, $(a)$ is the correct answer.