What would be the counterexample to the statement below:
IF THE SUM OF TWO INTEGERS IS EVEN, THEN BOTH OF THE INTEGERS ARE EVEN

Hello.

"A counter example demonstrates that an assertion is false and even
one counter example is enough to prove that an assertion is false. 
For example if an assertion is made that all dogs have four legs, and
a dog with three legs is found, then the assertion that all dogs have
four legs is proven incorrect."
http://www.mcoe.org/instruct/dm/glossary/counter_example.htm
------------

Now, consider the statement:
IF THE SUM OF TWO INTEGERS IS EVEN, THEN BOTH OF THE INTEGERS ARE EVEN

Here's a counter-example:

3 + 5 = 8.

Here, the sum of the two integer is even (i.e., 8), but the integers
(3 & 5) are NOT even.

search strategy: "counter example is"

I hope this helps.