The negation of the statement "The number is | vedclass

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Question

(A) Let $p$: The number is an odd number. Let $q$: The number is divisible by $3$. The given statement is $p \leftrightarrow q$. The negation of a bic

Vedclass · Accepted Answer

The number is an odd number but not divisible by $3$ or the number is divisible by $3$ but not odd.

Vedclass · Answer

(A) Let $p$: The number is an odd number. Let $q$: The number is divisible by $3$. The given statement is $p \leftrightarrow q$. The negation of a biconditional statement is $\sim(p \leftrightarrow q) \equiv (p \wedge \sim q) \vee (q \wedge \sim p)$. Thus,the negation is: "The number is an odd number but not divisible by $3$ $OR$ the number is divisible by $3$ but not an odd number."

The negation of the statement "The number is an odd number if and only if it is divisible by $3$."

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