Question

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

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

Answer 1

The correct option is C $(\sim p\wedge q)\vee \sim q$

$\to$ As $\sim (a\wedge b)=\sim a\vee \sim b$

$\Rightarrow \sim \left[\right(P\vee \sim q)\wedge q]$

$\Rightarrow \sim (P\vee \sim q)\vee (\sim q)$

$\Rightarrow (\sim P\wedge q)\vee (\sim q)\Rightarrow \left(C\right)$

$\because (\sim (P\vee q)=\sim P\wedge \sim q)$