Prove or disprove the average sum of two odd integers is even.

Question

Prove or disprove: The average of any two odd integers is even.

How do I start this?

I tried this one: The average of 1 and 3 is 2 which is even. so it's true.

is this the right way to prove the statement?

Answer 1

The correct way to prove a conjecture in mathematics is as follows:

• To prove the statement holds you have to show that it is true for all odd integers.
• To disprove the statement you only have to find one counter-example where the statement does not hold: $\cfrac{5+13}{2}=9\ne$ even integer.

Hence, you now conclude that you have disproved the statement.

QED.

(This is an abbreviation for the Latin phrase "quod erat demonstrandum" ("that which was to be demonstrated"), a notation which is often placed at the end of a mathematical proof to indicate its completion.) or you can use $\fbox{}$ instead.

Answer 2

$3+7\over2$$=5$. You should try some more examples.