Question

(i) Every prime number is odd.
(ii) The product of any two prime numbers is odd
Which of the above statement(s) is/are correct?
A. Statement (i) alone.
B. Statement (ii) alone.
C. Both statements (i) and (ii).
D. Neither statement (i) nor statement (ii).

Answer 1

Hint: At first we will learn about the prime numbers using the definition of prime numbers i.e. all those numbers that are only divisible by one and itself or we can say that numbers that have factors as 1 and the number itself only, we will judge the statements given to us whether they are correct or not.

Complete step by step answer:

Given data: Two statements that are to be checked whether they are correct or not i.e.
Every prime number is odd.
The product of any two prime numbers is odd.
Prime numbers are all those numbers that are only divisible by one and itself or we can say that numbers that have factors as 1 and the number itself only.
For example- 2, 3, 5 …..etc
For statement(i)
We know that the very first prime number is 2 which is a prime number as well as an even number and it is the only even prime number so statement (i) is incorrect.
For statement(ii)
We know that any number having 2 as a factor is an even number or any number which is a multiple of 2 is an even number since 2 is also a prime number if we multiply it with any other prime number the result will also be an even number, therefore, statement (ii) is also incorrect.
Since both the statements are incorrect
Option(D) is correct.

Note: Most of the students state both the statements correct as forgetting about the 2 as if we exclude 2 from the prime numbers, both the numbers will be correct as except 2 every prime number is odd, and except 2 product of any two number cannot have a factor of 2 making the product 2 so in that case both the statement would have been correct.