Question:
The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to:
Correct Option: 1
Solution:
$p: x \leftrightarrow \sim y=(x \rightarrow \sim y) \wedge(\sim y \rightarrow x)$
$=(\sim x \vee \sim y) \wedge(y \vee x)$
$=\sim(x \wedge y) \wedge(x \vee y)$ $(\because \sim(x \wedge y)=\sim x \vee \sim y)$
Negation of $p$ is
$\sim p=(x \wedge y) \vee \sim(x \vee y)=(x \wedge y) \vee(\sim x \wedge \sim y)$
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