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Negation

Let p, q, and...

Question

Let p,q, and r be any three logical statements. Which of the following is true?

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

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

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

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

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Solution

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

Only option C is correct. It is a direct application of Demorgan's law.

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

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