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Question: Answered & Verified by Expert
The negation of the proposition "If 2 is prime, then 3 is odd'" is
MathematicsMathematical ReasoningKCETKCET 2007
Options:
  • 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
Solution:
1007 Upvotes Verified Answer
The correct answer is: 2 is prime and 3 is not odd
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.

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