The negation of the compound proposition p ve | vedclass

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(D) The given proposition is $S = p \vee (\sim p \vee q)$.We need to find the negation $\sim S = \sim [p \vee (\sim p \vee q)]$.Using De Morgan's Law,

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None of these

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(D) The given proposition is $S = p \vee (\sim p \vee q)$.We need to find the negation $\sim S = \sim [p \vee (\sim p \vee q)]$.Using De Morgan's Law,$\sim (A \vee B) \equiv \sim A \wedge \sim B$,we get:$\sim S \equiv \sim p \wedge \sim (\sim p \vee q)$.Applying De Morgan's Law again to the second part,$\sim (\sim p \vee q) \equiv \sim (\sim p) \wedge \sim q \equiv p \wedge \sim q$.Therefore,$\sim S \equiv \sim p \wedge (p \wedge \sim q)$.Since the conjunction is associative,this is equivalent to $(\sim p \wedge p) \wedge \sim q$.Since $\sim p \wedge p$ is a contradiction $(F)$,the expression simplifies to $F \wedge \sim q$,which is $F$ (False).Looking at the options,none of the expressions provided are logically equivalent to $F$. Thus,the correct option is $D$.

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

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