Question

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

• A. The number is an odd number but not divisible by 3 or the number is divisible by 3 but not odd.
• B. The number is not an odd number iff it is not divisible by 3.
• C. The number is not an odd number but it is divisible by 3.
• D. The number is not an odd number or is not divisible by 3 but the number is divisible by 3 or odd.

Hint:

Logic Tip:In logic, the conjunctions but and and ($\wedge$) serve the exact same mathematical function.Always memorize the biconditional negation rule: $\sim(p \leftrightarrow q) \equiv (p \wedge \sim q) \vee (q \wedge \sim p)$.

Answer 1

The Correct Option is A