The negation of the boolean expression

Question:

The negation of the boolean expression $\sim \mathrm{s} \vee(\sim \mathrm{r} \wedge \mathrm{s})$ is equivalent to:

1. $\mathrm{r}$

2. $\mathrm{s} \wedge \mathrm{r}$

3. $\mathrm{s} \vee \mathrm{r}$

4. $\sim \mathrm{S} \wedge \sim \mathrm{r}$

Correct Option: , 2

Solution:

$\sim(\sim \mathrm{S} \vee(\sim \mathrm{r} \wedge \mathrm{S}))$

$\mathrm{s} \wedge(\mathrm{r} \vee \sim \mathrm{s})$

$(s \wedge r) \vee(s \wedge \sim s)$

$(s \wedge r) \vee(c)$

$(s \wedge r)$