Question

Find a pair of numbers that provides a counterexample to show that the given statement is false. (Enter your answers as a comma-separated list.) If the sum of two counting numbers is an even counting number, then the product of the two counting numbers is an even counting number

Answer 1

Answer:

Step-by-step explanation:

We have to find a pair of numbers which give sum as even number but product is not even.

We know even numbers are multiples of 2.

When we add two even numbers we get even number and their product also would be even.

Similarly when we add two odd numbers we get answer as even number

Eg. $1+1=2\\3+3=6\\2k+1 +(2k+3) = 4k+4 i.e. even$

But product need not be even.

We have

$1+3=4 even\\1(3) =3 not even$

Thus we have given counter example that when sum of two counting numbers is even, product need not be even.