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  4. The proposition ∼(p Leftrightarrow q) is equivalent to

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

Bihar CECEBihar CECE 2013

Solution:

$\sim(p \Leftrightarrow q) \equiv \sim[(p \Rightarrow q) \wedge(q \Rightarrow p)] $
$ \equiv \sim(p \Rightarrow q) \vee(\sim(q \Rightarrow p)) $
($\because$ by De-Morgan's law )
$\equiv(p \wedge \sim q) \vee(q \wedge \sim p)$