The negation of the Boolean expression
Question:

The negation of the Boolean expression $p \vee(\sim p \wedge q)$ is equivalent to:

  1. (1) $p \wedge \sim q$

  2. (2) $\sim p \wedge \sim q$

  3. (3) $\sim p \vee \sim q$

  4. (4) $\sim p \vee q$


Correct Option: , 2

Solution:

Negation of given statement $=\sim(p \vee(\sim p \wedge q))$

$=\sim p \wedge \sim(\sim p \wedge q)=\sim p \wedge(p \vee \sim q)$

$=(\sim p \wedge q) \vee(\sim p \wedge \sim q)$

$=F \vee(\sim p \wedge \sim q)=\sim p \wedge \sim q$

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