Negation of the Boolean expression p Leftrigh | vedclass

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(D) We want to find the negation of the expression $p \Leftrightarrow (q \Rightarrow p)$.Let $S = p \Leftrightarrow (q \Rightarrow p)$.Using the prope

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$(\sim p) \wedge (\sim q)$

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(D) We want to find the negation of the expression $p \Leftrightarrow (q \Rightarrow p)$.Let $S = p \Leftrightarrow (q \Rightarrow p)$.Using the property $\sim(A \Leftrightarrow B) = (A \wedge \sim B) \vee (B \wedge \sim A)$,we have:$\sim S = (p \wedge \sim(q$ $\Rightarrow p)) \vee ((q$ $\Rightarrow p) \wedge \sim p)$.Now,simplify the first part: $p \wedge \sim(q \Rightarrow p) = p \wedge (q \wedge \sim p) = (p \wedge \sim p) \wedge q = F \wedge q = F$ (where $F$ is a contradiction).Simplify the second part: $(q$ $\Rightarrow p) \wedge \sim p = (\sim q \vee p) \wedge \sim p = (\sim q \wedge \sim p) \vee (p \wedge \sim p) = (\sim p \wedge \sim q) \vee F = \sim p \wedge \sim q$.Combining these,$\sim S = F \vee (\sim p \wedge \sim q) = \sim p \wedge \sim q$.

Negation of the Boolean expression $p \Leftrightarrow (q \Rightarrow p)$ is:

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