Question

The negation of proposition ‘ if 2 is prime, then 3 is odd’ is
( a) If 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) If 2 is not prime, then 3 is odd.

Answer 1

Hint: This question is based on a negation of a statement. It is a statement which contains a variable and becomes either true or false depending on the value which changes the variable . To solve this question, we put the properties of negative statements and check which options follow our answer.

Complete step by step solution: 
To solve these types of questions, we first know the proper meaning of negation of propositions.
A statement is a relevant sentence that is not an exclamation, or question or order. A statement is appropriate only if it is either invariably true or invariably false. Generally in mathematics, it is necessary to seek out the other of the given statement. The method of finding the other of the given statement is termed as negation.
Given statement is If 2 is prime, then 3 is odd.
We have to tell the negation of a given proposition.
Let p = 2 is prime and
Q = 3 is odd
P $\to $ Q = 2 is prime, then 3 is odd.
 Then the Negation of P $\to $ Q is $(p\to q)$
Negation of $p\to q$is $\sim (p\to q)$$\cong p\wedge \sim q$
This means $p\to q$ is $\cong p\wedge \sim q$
That means 2 is prime and 3 is not odd.
Option (B) is correct.

Note: to solve these types of questions, students must know the proper meaning of negation. Students must have the deep knowledge of using each symbol then he is able to solve this type of question.