Which of the following statements is logicall | vedclass

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(D) The biconditional statement $p \leftrightarrow q$ is equivalent to $(p 	o q) \land (q 	o p)$.Thus, $∼ (p \leftrightarrow q) \equiv ∼ ((p 	o q)

Vedclass · Accepted Answer

$p \leftrightarrow ∼ q$

Vedclass · Answer

(D) The biconditional statement $p \leftrightarrow q$ is equivalent to $(p 	o q) \land (q 	o p)$.Thus, $∼ (p \leftrightarrow q) \equiv ∼ ((p 	o q) \land (q 	o p))$.Using De Morgan's Law, this becomes $∼ (p 	o q) \lor ∼ (q 	o p)$.Since $p 	o q \equiv ∼ p \lor q$, then $∼ (p 	o q) \equiv p \land ∼ q$.Similarly, $∼ (q 	o p) \equiv q \land ∼ p$.So, $∼ (p \leftrightarrow q) \equiv (p \land ∼ q) \lor (q \land ∼ p)$.Now, check option $(D)$: $p \leftrightarrow ∼ q \equiv (p 	o ∼ q) \land (∼ q 	o p)$$\equiv (∼ p \lor ∼ q) \land (q \lor p)$$\equiv (∼ p \land q) \lor (∼ p \land p) \lor (∼ q \land q) \lor (∼ q \land p)$$\equiv (∼ p \land q) \lor F \lor F \lor (p \land ∼ q)$$\equiv (p \land ∼ q) \lor (q \land ∼ p)$.Thus, $∼ (p \leftrightarrow q) \equiv p \leftrightarrow ∼ q$.

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

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