The negation of the Boolean expression x left | vedclass

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Question

(C) The given expression is $x \leftrightarrow \sim y$.We know that $p \leftrightarrow q \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$.So,$x

Vedclass · Accepted Answer

$(x \wedge y) \vee (\sim x \wedge \sim y)$

Vedclass · Answer

(C) The given expression is $x \leftrightarrow \sim y$.We know that $p \leftrightarrow q \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$.So,$x \leftrightarrow \sim y \equiv (x$ $\rightarrow \sim y) \wedge (\sim y$ $\rightarrow x)$.Using the identity $p \rightarrow q \equiv \sim p \vee q$,we get:$x \leftrightarrow \sim y \equiv (\sim x \vee \sim y) \wedge (y \vee x)$.Now,we find the negation:$\sim(x \leftrightarrow \sim y) \equiv \sim((\sim x \vee \sim y) \wedge (x \vee y))$.By De Morgan's Law,$\sim(A \wedge B) \equiv \sim A \vee \sim B$:$\sim(x \leftrightarrow \sim y) \equiv \sim(\sim x \vee \sim y) \vee \sim(x \vee y)$.Applying De Morgan's Law again:$\sim(x \leftrightarrow \sim y) \equiv (x \wedge y) \vee (\sim x \wedge \sim y)$.

The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to

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