Question

For any two statements $p$ and $q$, the negation of the expression $p\vee (\sim p\wedge q)$ is :

• A. $\sim p\vee \sim q$
• B. $\sim p\wedge \sim q$
• C. $p\vee q$
• D. $p\leftrightarrow q$

Answer 1

The correct option is B $\sim p\wedge \sim q$

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