Answer:
The statement is false.
Step-by-step explanation:
Let a and b represent two odd integers.
The average (A) is defined by:
A=[tex]\frac{a+b}{2}[/tex]
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= [tex]\frac{3+5}{2} = \frac{8}{2} = 4[/tex]
The result of the average is even, therefore the statement is false.
The previous calculation is a counterexample.
