jtkline2001
contestada

Consider the conditional statement shown.

If any two numbers are prime, then their product is odd.

What number must be one of the two primes for any counterexample to the statement?

a) 2
b) 6
c) 7
d) 10

Respuesta :

Hello!

First of all, 6 and 10 are not prime numbers as they both have at least two pairs of factors (one factor pair plus one and itself). 

Anything multiplied by two is even. Therefore, a) 2 counterexamples the statement. Just to show why 7 doesn't work, seven multiplied by 3 is 21, which is odd, and 7 times 7 is 49, and 7 times 5 is 35 (all prime multipliers). The only one that works is two.

I hope this helps!
varshamittal029

The correct option is option A: 2 is one of the two primes for any counterexample to the statement.

What is prime number?

The number whose number of factors is only 2 which is 1 and the number itself, is called a prime number.

For example, 2,3,5,7... are examples of prime number.

Here, The statement is If any two numbers are prime, then their product will be odd.

The counter-statement will be the two numbers are prime but their product is even.

As we know for the product of the two numbers to be even, one of the two numbers is even.

Here that number has to be also a prime number.

So there is only one number which is prime as well as the even number is 2.

checking all the options,

A. 2: This is prime as well as even, so this correct option.

B. 6: This is not prime as it has more than 2 factors, so this is not the correct option.

C. 7: As the product of 7 and any number is not even, so this is not the correct option.

D. 10: This is not prime as it has more than 2 factors, so this is not the correct option.

Therefore, 2 is one of the two primes for counterexample to this statement.

Learn more about prime number

here: https://brainly.com/question/145452

#SPJ2

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