The contrapositive of the statement pattern [ | vedclass

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Question

(D) The contrapositive of a conditional statement $A 	o B$ is defined as $\sim B 	o \sim A$.Here, $A = [p \lor (p 	o q)]$ and $B = (p \land \sim q)

Vedclass · Accepted Answer

$(\sim p \lor q) 	o [\sim p \land (p \land \sim q)]$

Vedclass · Answer

(D) The contrapositive of a conditional statement $A 	o B$ is defined as $\sim B 	o \sim A$.Here, $A = [p \lor (p 	o q)]$ and $B = (p \land \sim q)$.First, find $\sim B$: $\sim(p \land \sim q) \equiv \sim p \lor \sim(\sim q) \equiv \sim p \lor q$.Next, find $\sim A$: $\sim[p \lor (p 	o q)] \equiv \sim p \land \sim(p 	o q)$.Since $(p 	o q) \equiv (\sim p \lor q)$, then $\sim(p 	o q) \equiv \sim(\sim p \lor q) \equiv (p \land \sim q)$.Thus, $\sim A \equiv \sim p \land (p \land \sim q)$.Therefore, the contrapositive $\sim B 	o \sim A$ is $(\sim p \lor q) 	o [\sim p \land (p \land \sim q)]$.

The contrapositive of the statement pattern $[p \lor (p \to q)] \to (p \land \sim q)$ is

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