Question:
The negation of the Boolean expression $p \vee(\sim p \wedge q)$ is equivalent to :
Correct Option: , 3
Solution:
Negation of $\phi \vee(\sim p \wedge q)$
$\mathrm{p} \vee(\sim \mathrm{p} \wedge \mathrm{q})=(\mathrm{p} \vee \sim \mathrm{p}) \wedge(\mathrm{p} \vee \mathrm{q})$
$=(\mathrm{T}) \wedge(\mathrm{p} \vee \mathrm{q})$
$=(\mathrm{p} \vee \mathrm{q})$
now negation of $(\mathrm{p} \vee \mathrm{q})$ is
$\sim(\mathrm{p} \vee \mathrm{q})=\sim \mathrm{p} \wedge \sim \mathrm{q}$
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