Question

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

• A. $(p\mspace{6mu} \land \sim q)\mspace{6mu} \land \sim p$
• B. $(p\mspace{6mu} \land \sim q)\mspace{6mu} \vee \sim p$
• C. $(p\mspace{6mu} \vee \sim q)\mspace{6mu} \vee \sim p$
• D. None of these

Answer 1

Answer: (A)

$(p\mspace{6mu} \land \sim q)\mspace{6mu} \land \sim p$

Answer 2

$\sim\lbrack p \vee (\sim p \vee q)\rbrack \equiv \sim p\mspace{6mu} \land \sim(\sim p \vee q)$

$\equiv \mspace{6mu}\sim p \land (\sim(\sim p)\mspace{6mu} \land \sim q)$

$\equiv \sim p \land (p\mspace{6mu} \land \sim q)$.