Question

The contrapositive statement of the statement “If x is a prime number, then x is odd” is:
(a) If x is not a prime number, then x is not odd
(b) If x is not odd, then x is not a prime number
(c) If x is a prime number, then x is not odd
(d) If x is not a prime number, then x is odd

Answer 1

Hint: To find the appropriate answer to this question, we should know what the contrapositive statement is. Contrapositive statements are statements formed by contradicting both the hypothesis and conclusion of a given proposition and then interchanging them.

Complete step-by-step answer:
In this question, we have to find the contrapositive statement of the statement, “If x is a prime number, then x is odd”. We know that contrapositive statements are statements formed by contradicting both the hypothesis and conclusion of a given proposition and then interchanging them. For example, the contrapositive of “if A then B’’ is “If not B then not A”.
In the question, the statement is “If x is a prime number, then x is an odd number”. So, let us consider A = x is prime number and B = x is odd. Then according to the rules of contrapositive statement, we can say that the contrapositive of the given statement is “If x is not odd, then x is not a prime number”.
Hence, option (b) is the right answer.

Notes: In a hurry, one can choose option (a) as the correct answer but it is not because option (a) states that if a number is not a prime number, then it is not an odd number. But the given statement states that if a number is a prime number, then the number is odd. So, we can see that the option (a) and the given statements are vice – versa and not contrapositive statements.