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(C) The logical equivalence $(p \Rightarrow q) \equiv (\sim p \vee q)$ is a standard identity. Applying the negation operator to both sides: $\sim (p

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

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(C) The logical equivalence $(p \Rightarrow q) \equiv (\sim p \vee q)$ is a standard identity. Applying the negation operator to both sides: $\sim (p \Rightarrow q) \equiv \sim (\sim p \vee q)$ Using De Morgan's Law,$\sim (A \vee B) \equiv (\sim A \wedge \sim B)$: $\sim (p \Rightarrow q) \equiv (\sim (\sim p) \wedge \sim q)$ Since $\sim (\sim p) \equiv p$,we get: $\sim (p \Rightarrow q) \equiv (p \wedge \sim q)$ Both options $A$,$C$,and $D$ are logically valid identities. However,in standard logic textbooks,these are all tautologies. Given the structure,$C$ is a fundamental definition of the negation of a conditional statement.

Which of the following logical equivalences is always true?

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