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Natasha2012 [34]
3 years ago
15

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.
Mathematics
1 answer:
natta225 [31]3 years ago
3 0

Answer:

The statement is false.

Step-by-step explanation:

Let a and b represent two odd integers.

The average (A) is defined by:

A=\frac{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= \frac{3+5}{2} = \frac{8}{2} = 4

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

The previous calculation is a counterexample.

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