Which of the following statements is logicall | vedclass

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(D) Step $1$: The biconditional statement $p \leftrightarrow q$ is equivalent to $(p 	o q) \land (q 	o p)$.Step $2$: The negation $\sim (p \leftrigh

Vedclass · Accepted Answer

$p \leftrightarrow \sim q$

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(D) Step $1$: The biconditional statement $p \leftrightarrow q$ is equivalent to $(p 	o q) \land (q 	o p)$.Step $2$: The negation $\sim (p \leftrightarrow q)$ is equivalent to $\sim ((p 	o q) \land (q 	o p))$.Step $3$: By De Morgan's Law, this becomes $\sim (p 	o q) \lor \sim (q 	o p)$.Step $4$: Since $\sim (p 	o q) \equiv p \land \sim q$, the expression becomes $(p \land \sim q) \lor (q \land \sim p)$.Step $5$: This is the definition of the exclusive $OR$ $(p \oplus q)$, which is logically equivalent to $p \leftrightarrow \sim q$ or $\sim p \leftrightarrow q$.Step $6$: Comparing with the options, $p \leftrightarrow \sim q$ is option $D$.

Which of the following statements is logically equivalent to $\sim (p \leftrightarrow q)$?

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