Question:
The negation of the Boolean expression $\mathrm{x} \leftrightarrow \sim \mathrm{y}$ is equivalent to:
Correct Option: , 3
Solution:
$p \leftrightarrow q \equiv(p \rightarrow q) \wedge(q \rightarrow p)$
$x \leftrightarrow \sim y \equiv(x \rightarrow \sim y) \wedge(-y \rightarrow x)$
$\because(p \rightarrow q \equiv \sim p \vee q)$
$\mathrm{X} \leftrightarrow \sim \mathrm{y}=(\sim \mathrm{X} \vee \sim \mathrm{y}) \wedge(\mathrm{y} \vee \mathrm{x})$
$\sim(x \leftrightarrow \sim y)=(x \wedge y) \vee(\sim x \wedge \sim y)$
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