Question

4. Determine whether the statement is true or false. Prove the statement directly from the definition if it is true, and give a counterexample if it is false. The average of two odd integers is odd.

Answer 1

The statement is false.

Explanation:

Let a and b represent two odd integers.

The average (A) is defined by:

A=
`(a+b)/(2)`

In order to prove the statement, you have to show that it's true for all odd integers. But, to disprove it, you just have to find a counterexample where the statement is false.

Notice that it is easier to try to find a counterexample.

For example, a=3 and b=5

A=
`(3+5)/(2) = (8)/(2) = 4`

The result of the average is even, therefore the statement is false.

The previous calculation is a counterexample.