Question

Which of the following is the inverse of the proposition: “if a number is a prime then it is odd”.
A. If a number is not a prime then it is odd
B. If a number is not a prime then it is not odd
C. If a number is not odd then it is not a prime
D. If a number is not odd then it is prime

Answer 1

Hints First suppose that p stands for a number is prime and q stands for it is odd, then to obtain the inverse just state the opposite form of the statement p and q.

Complete step by step solution
The given statement is “if a number is a prime then it is odd”.
Suppose, p= A number is prime and q=it is odd.
Then we are given that \[p \to q\] .
We have to obtain the inverse of the given proposition that is \[ \sim p \to \sim q\] .
Now, \[ \sim p\] is “A number is not prime” and \[ \sim q\] is “it is jot odd”.
Therefore, the inverse proposition is “If a number is not prime then it is not odd.”
The correct option is B.

Note Sometimes students get confused if we have to take the inverse of both the statements or if we can take the only inverse of one statement. So for the inverse proposition, we have to take the inverse of both the statements.