Question

For any two statements p and q, the statement $\sim (p\vee q)\vee (\sim p\wedge q)$ is equivalent to

• A. $\sim p$
• B. $p$
• C. q
• D. $\sim q$

Answer 1

The correct option is A

$\sim p$

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