Answer: The correct option is
(C) The number 2 is prime, and the product of 2 and 2 is 4.
Step-by-step explanation: We are given to select the correct counter example that shows that the following conjecture is false :
“the product of two prime numbers is odd”
Option (A) : The given statement is
"The numbers 3 and 7 are both prime, and their product is odd".
This does not show that the given conjecture is false, because here the product of both the primes is odd, not even.
So, this option is NOT correct.
Option (B) : The given statement is
"The number 2 is prime, but the product of 2 and 6 is 120".
This does not show that the given conjecture is false, because here the number 6 is not prime.
So, this option is NOT correct.
Option (C) : The given statement is
"The number 2 is prime, and the product of 2 and 2 is 4".
This does shows that the given conjecture is false, because here the number 2 is prime, and the product of 2 and 2 is even, not odd.
So, this option is CORRECT.
Option (D) : The given statement is
"The number 2 is a prime number, and it is an even number".
This does not show that the given conjecture is false, because here we are not considering the product of two prime numbers.
So, this option is NOT correct.
Thus, (C) is the correct option.
