Question:
For any two statements $\mathrm{p}$ and $\mathrm{q}$, the negation of the expression $p \vee(\sim p \wedge q)$ is
Correct Option: , 4
Solution:
$\sim(\mathrm{p} \vee(\sim \mathrm{p} \wedge \mathrm{q}))$
$=\sim \mathrm{p} \wedge \sim(\sim \mathrm{p} \wedge \mathrm{q})$
$=\sim \mathrm{p} \wedge(\mathrm{p} \vee \sim \mathrm{q})$
$=(\sim \mathrm{p} \wedge \mathrm{p}) \vee(\sim \mathrm{p} \wedge \sim \mathrm{q})$
$=\mathrm{c} \vee(\sim \mathrm{p} \wedge \sim \mathrm{q})$
$=(\sim \mathrm{p} \wedge \sim \mathrm{q})$