Question

The negation of the statement $\sim p\wedge (p\vee q)$ is

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

Answer 1

The correct option is D $p\vee \sim q$

Negation of $\sim p\wedge (p\vee q)$ is
$\sim [\sim p\wedge (p\vee q\left)\right]$
$\equiv p\vee \sim (p\vee q)$
$\equiv p\vee (\sim p\wedge \sim q)$
$\equiv (p\vee \sim p)\wedge (p\vee \sim q)$
$\equiv T\wedge (p\vee \sim q)$, where $T$ is tautology.
$\equiv p\vee \sim q$