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Question

The negation of the proposition: "If 2 is a prime number then 3 is a odd number" is


A

if 2 is not prime, then 3 is not odd

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B

2 is prime and 3 is not odd

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C

2 is not prime and 3 is odd

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D

if 2 is not prime, then 3 is odd

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Solution

The correct option is B

2 is prime and 3 is not odd


Explanation for the correct answer:

Let p denote the statement that 2 is a prime number

Let q denote the statement that 3 is a odd number

The given statement is that, " If 2 is a prime number then 3 is a odd number"

This statement can be written in Boolean format as

pq

Now to find the negation of this statement

~pqp~q

Now this Boolean expression is written in word format again as,

2 is prime and 3 is not odd.

Hence, option B is the correct answer.


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