Which of the following is true?

p \land q = p \lor q

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(p \land q \lor r) \Leftrightarrow (p \lor q) \land r

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\sim (p \land q) \Leftrightarrow\sim p \lor \sim q

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\sim p =\sim q

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Solution

The correct option is C $\sim (p \land q) \Leftrightarrow\sim p \lor \sim q$
$p \land q = p \lor q$
Clearly, this is false for $p = T, q = F$

$(p \lor q) \land r = (p \land r) \lor (q \land r) \neq (p \land q \land r)$

$\sim (p \land q) \Leftrightarrow\sim p \lor \sim q$
Clearly, this is true as it is De-Morgan's Law.

$\sim p =\sim q$ is false when $p = T, q = F$

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