The negative of the statement
Question:

The negative of the statement $\sim \mathrm{p} \wedge(\mathrm{p} \vee \mathrm{q})$ is

1. $\sim \mathrm{p} \vee \mathrm{q}$

2. $\mathrm{p} \vee \sim \mathrm{q}$

3. $\sim \mathrm{p} \wedge \mathrm{q}$

4. $p \wedge \sim q$

Correct Option: , 2

Solution:

$\sim(\sim \mathrm{p} \wedge(\mathrm{p} \vee \mathrm{q}))$

$\mathrm{p} \vee(\sim \mathrm{p} \wedge \sim \mathrm{q})$

$\underbrace{(p v \sim p)}_{t} \wedge(p v \sim q)$

$\mathrm{p} \vee \sim \mathrm{q}$