KCET · Maths · Mathematical Reasoning
The negation of the proposition "If 2 is prime, then 3 is odd'" is
- A 2 is not prime, then 3 is not odd
- B 2 is prime and 3 is not odd
- C 2 is not prime and 3 is odd
- D is 2 is not prime, then 3 is odd
Answer & Solution
Correct Answer
(B) 2 is prime and 3 is not odd
Step-by-step Solution
Detailed explanation
Let \(p=2\) is prime
\(q=3\) is odd
\(p \rightarrow q=2\) is prime, then 3 is odd.
Negation of \(P \rightarrow q\) is \(\sim(p \rightarrow q)\)
\(\Rightarrow \quad p \wedge \sim q\)
\(\Rightarrow 2\) is prime and 3 is not odd.
\(q=3\) is odd
\(p \rightarrow q=2\) is prime, then 3 is odd.
Negation of \(P \rightarrow q\) is \(\sim(p \rightarrow q)\)
\(\Rightarrow \quad p \wedge \sim q\)
\(\Rightarrow 2\) is prime and 3 is not odd.
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