MHT CET 2023 Mathematics question

Not in JEE syllabus

The negation of the statement "The number is an odd number if and only if it 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.Correct
(B)The number is not an odd number if 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.

Answer: (A)

Solution

Let : "the number is odd" and : "the number is divisible by 3". The statement is . Since , its negation is . In words: "the number is odd but not divisible by 3, or it is

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Question ID VK-098355