MHT CET · Maths · Mathematical Reasoning
The negation of the statement "The number is an odd number if and only if it is divisible by \(3\) . "
- A (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.
Answer & Solution
Correct Answer
(A) (A) The number is an odd number but not divisible by 3 or the number is divisible by 3 but not odd.
Step-by-step Solution
Detailed explanation
Let \(\mathrm{p}\) : The number is an odd number,
\(\mathrm{q}:\) The number is divisible by 3
\(
\sim(p \leftrightarrow q) \equiv(p \wedge \sim q) \vee(q \wedge \sim p)
\)
\(\therefore \quad\) The negation of the given statement is "The number is an odd number but not divisible by 3 or the number is divisible by 3 but not odd'.
\(\mathrm{q}:\) The number is divisible by 3
\(
\sim(p \leftrightarrow q) \equiv(p \wedge \sim q) \vee(q \wedge \sim p)
\)
\(\therefore \quad\) The negation of the given statement is "The number is an odd number but not divisible by 3 or the number is divisible by 3 but not odd'.
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