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(D) The logical equivalence for the biconditional statement is $(p \leftrightarrow q) \equiv (p 	o q) \land (q 	o p)$.We know that $\sim (p \leftrig

Vedclass · Accepted Answer

$p \leftrightarrow \sim q$

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(D) The logical equivalence for the biconditional statement is $(p \leftrightarrow q) \equiv (p 	o q) \land (q 	o p)$.We know that $\sim (p \leftrightarrow q)$ is equivalent to $p \leftrightarrow \sim q$ or $\sim p \leftrightarrow q$.Let us verify the truth table for $\sim (p \leftrightarrow q)$:If $p=T, q=T$, then $\sim (T \leftrightarrow T) = \sim (T) = F$.If $p=T, q=F$, then $\sim (T \leftrightarrow F) = \sim (F) = T$.If $p=F, q=T$, then $\sim (F \leftrightarrow T) = \sim (F) = T$.If $p=F, q=F$, then $\sim (F \leftrightarrow F) = \sim (T) = F$.Now check option $(D)$: $p \leftrightarrow \sim q$.If $p=T, q=T$, then $T \leftrightarrow F = F$.If $p=T, q=F$, then $T \leftrightarrow T = T$.If $p=F, q=T$, then $F \leftrightarrow F = T$.If $p=F, q=F$, then $F \leftrightarrow T = F$.Since the truth values match, $\sim (p \leftrightarrow q) \equiv p \leftrightarrow \sim q$.

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

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

Similar Questions

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