The negation of the contrapositive of the sta | vedclass

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(D) Let $S$ be the statement $(p \lor \sim q) 	o (p \land \sim q)$.The contrapositive of $A 	o B$ is $\sim B 	o \sim A$.Thus, the contrapositive of

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$(\sim p \lor q) \land (p \lor \sim q)$

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(D) Let $S$ be the statement $(p \lor \sim q) 	o (p \land \sim q)$.The contrapositive of $A 	o B$ is $\sim B 	o \sim A$.Thus, the contrapositive of $S$ is $\sim (p \land \sim q) 	o \sim (p \lor \sim q)$.Using De Morgan's laws, this is $(\sim p \lor q) 	o (\sim p \land q)$.The negation of an implication $P 	o Q$ is $P \land \sim Q$.Here, $P = (\sim p \lor q)$ and $Q = (\sim p \land q)$.Negation $= (\sim p \lor q) \land \sim (\sim p \land q)$.Applying De Morgan's law to the second part: $\sim (\sim p \land q) = (p \lor \sim q)$.Therefore, the negation is $(\sim p \lor q) \land (p \lor \sim q)$.

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

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