The contrapositive of the statement pattern [ | vedclass

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(D) The contrapositive of a statement $A 	o B$ is $\sim B 	o \sim A$.Here, $A = [p \lor (p 	o q)]$ and $B = (p \land \sim q)$.Step $1$: Find $\sim

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

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(D) The contrapositive of a statement $A 	o B$ is $\sim B 	o \sim A$.Here, $A = [p \lor (p 	o q)]$ and $B = (p \land \sim q)$.Step $1$: Find $\sim B = \sim (p \land \sim q) = (\sim p \lor \sim (\sim q)) = (\sim p \lor q)$.Step $2$: Find $\sim A = \sim [p \lor (p 	o q)] = \sim p \land \sim (p 	o q)$.Since $\sim (p 	o q) = (p \land \sim q)$, we have $\sim A = \sim p \land (p \land \sim q)$.Step $3$: The contrapositive is $\sim B 	o \sim A$, which is $(\sim p \lor q) 	o [\sim p \land (p \land \sim q)]$.Note: The provided options in the input were incomplete/incorrect. The correct logical form is $(\sim p \lor q) 	o [\sim p \land (p \land \sim q)]$, which matches the structure of option $D$ after correction.

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

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