The negation of the contrapositive of the sta | vedclass

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Question

(A) Let $S$ be the statement $(p \lor \sim q) 	o (p \land \sim q)$.$1$. The contrapositive of $A 	o B$ is $\sim B 	o \sim A$.$2$. The contrapositiv

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

Vedclass · Answer

(A) Let $S$ be the statement $(p \lor \sim q) 	o (p \land \sim q)$.$1$. The contrapositive of $A 	o B$ is $\sim B 	o \sim A$.$2$. The contrapositive of $S$ is $\sim (p \land \sim q) 	o \sim (p \lor \sim q)$.$3$. Using De Morgan's laws, this is $(\sim p \lor q) 	o (\sim p \land q)$.$4$. The negation of $P 	o Q$ is $P \land \sim Q$.$5$. The negation of the contrapositive is $(\sim p \lor q) \land \sim (\sim p \land q)$.$6$. Applying De Morgan's law again, $\sim (\sim p \land q) = (p \lor \sim q)$.$7$. Thus, the result 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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