Question

Identify a counterexample: If the sum of two integers is even, then both the integers are even
6+ 10 = 16
3+9 = 12
14 + 9 = 23
none of these

Answer 1

Answer:

3+9 = 12

Explanation:

A "counterexample" is an example that shows the falseness of a statement.

Among the choices above, 3+9 = 12 is the ideal counterexample. Its sum is an even integer (12); however, its addends are odd integers (3 and 9). So, this goes against the statement above.

The first choice (6+10 = 16) is clearly not a counterexample, but an example of the statement. The second choice (14+9=23) is not a counterexample because its product is an odd integer, not an even integer. The statement is referring to the condition of an even integer for an answer.