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Distributive Law

For any two s...

Question

For any two statements p and q, the negation of the expression $p \lor (\sim p \land q)$ is?

p \land q

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p \leftrightarrow q

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\sim p \lor \sim q

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\sim p \land \sim q

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Solution

The correct option is B $\sim p \land \sim q$
$\sim (p \lor (\sim p \land q))$

$=\sim p \land \sim (\sim p \land q)$
$=\sim p \land (p \lor \sim q)$

$= (\sim p \land p) \lor (\sim p \land \sim q)$

$= F \lor (\sim p \land \sim q)$

$= (\sim p \land \sim q)$ .

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