The Boolean expression (p Rightarrow q) wedge | vedclass

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Question

(D) We are given the expression $(p$ $\Rightarrow q) \wedge (q$ $\Rightarrow \sim p)$.Using the logical equivalence $(A \Rightarrow B) \equiv (\sim A

Vedclass · Accepted Answer

$\sim p$

Vedclass · Answer

(D) We are given the expression $(p$ $\Rightarrow q) \wedge (q$ $\Rightarrow \sim p)$.Using the logical equivalence $(A \Rightarrow B) \equiv (\sim A \vee B)$,we rewrite the expression:$(\sim p \vee q) \wedge (\sim q \vee \sim p)$Using the commutative property,we rearrange the terms:$(\sim p \vee q) \wedge (\sim p \vee \sim q)$Applying the distributive property,we factor out $(\sim p \vee)$:$\sim p \vee (q \wedge \sim q)$Since $(q \wedge \sim q)$ is a contradiction (always false),the expression becomes:$\sim p \vee F \equiv \sim p$Therefore,the expression is equivalent to $\sim p$.

The Boolean expression $(p$ $\Rightarrow q) \wedge (q$ $\Rightarrow \sim p)$ is equivalent to:

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