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Logical Connectives

The dual of s...

Question

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

A

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

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B

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

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C

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

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D

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

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Solution

The correct option is A
$p \land (q \lor r) \equiv (p \land q) \lor (p \land r)$

By definition of duality, replace $\land$ by $\lor$ and $\lor$ by $\land$
So, dual of $p \land (q \lor r) \equiv (p \land q) \lor (p \land r)$

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Logical Connectives

Standard XII Mathematics

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