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

\sim [p \land (\sim q)] \equiv (\sim p) \land q

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\sim (p \lor q) \land (\sim r) \equiv (\sim p) \lor (\sim q) \lor (\sim r)

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\sim [p \lor (\sim q)] \equiv (\sim p) \land q

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\sim [p \land (\sim q)] \equiv (\sim p) \land \sim q

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\sim [p \land (\sim q)] \equiv p \land q

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Solution

The correct option is C $\sim [p \lor (\sim q)] \equiv (\sim p) \land q$
$\sim [p \land (\sim q)] \equiv (\sim p) \lor \sim (\sim q) \equiv (\sim p) \lor q$

So option $A$ is not correct

$\sim (p \lor q) \land (\sim r) \equiv (\sim p) \land (\sim q) \land (\sim r)$

So option $B$ is also not correct.
$\sim [p \lor (\sim q)] \equiv (\sim p) \land \sim (\sim q) \equiv (\sim p) \land q$

So option $C$ is correct.

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Similar questions

p, q, r

p \Rightarrow (q \lor r)

[\sim (\sim p \lor q) \lor (p \land r)] \land (\sim q \land r)

The dual of statement $p \lor (q \land r) \equiv (p \lor q) \land (p \lor r)$ is

P : [(⇁ p \lor q) \land (r \to s) \land (p \lor r)] \to (⇁ s \to q)

Q : [(⇁ p \land q) \land [q \to (p \to r)]] \to⇁ r

R : [[(q \land r) \to p] \land (⇁ q \lor p)] \to r

S : [p \land (p \to r) \land (q \lor ⇁ r)] \to q

Factorise: $(p^{2} + q^{2} - r^{2})^{2} - 4 p^{2} q^{2}$

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