The negation of the compound statement sim p | vedclass

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(A) The negation of the statement $\sim p \vee (p \vee (\sim q))$ is given by $\sim (\sim p \vee (p \vee \sim q))$.Using De Morgan's Law,$\sim (A \vee

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

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(A) The negation of the statement $\sim p \vee (p \vee (\sim q))$ is given by $\sim (\sim p \vee (p \vee \sim q))$.Using De Morgan's Law,$\sim (A \vee B) \equiv \sim A \wedge \sim B$,we get:$p \wedge \sim (p \vee \sim q)$.Applying De Morgan's Law again,$\sim (p \vee \sim q) \equiv \sim p \wedge \sim (\sim q) \equiv \sim p \wedge q$.Thus,the expression becomes $p \wedge (\sim p \wedge q)$.By the associative property,this is equivalent to $(p \wedge \sim p) \wedge q$,which is $F \wedge q = F$.However,evaluating the options provided,the expression $(\sim p \wedge q) \wedge p$ is equivalent to $(\sim p \wedge p) \wedge q = F \wedge q = F$. Both the original negation and option $A$ evaluate to a contradiction.

The negation of the compound statement $\sim p \vee (p \vee (\sim q))$ is

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