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Associative Law

The logical s...

Question

The logical statement $[\sim (\sim p \lor q) \lor (p \land r)] \land (\sim q \land r)$ is equivalent to :

A

\sim p \lor r

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B

(p \land r) \land \sim q

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C

(p \land \sim q) \lor r

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D

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

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Solution

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

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p, q, r

denote the arbitary statements then the logical equivalance of the statement

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Q. The logical statement

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

is equivalent to:

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

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(p \lor q) \land r

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Associative Law

Standard XII Mathematics

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