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Logical Connectives

The propositi...

Question

The proposition $\sim (p \Leftrightarrow q)$ is equivalent to

A

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

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B

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

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C

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

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D

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

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Solution

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

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Logical Connectives

Standard XII Mathematics

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