The sum of any two even integers is divisible by 4. 2. Which of the following pairs of integers can be used as a counterexample to show that the statement above is false? (A) 2 and 6 (B) 3 and 7 (C) 4 and 4 (D) 6 and 8 (E) 8 and 9

The correct answer is (E) 8 and 9.<br /><br />To explain why this pair of integers can be used as a counterexample to show that the statement "The sum of any two even integers is divisible by 4" is false, let's first understand what a counterexample is. A counterexample is an example that disproves a statement or proposition.<br /><br />In this case, the statement claims that the sum of any two even integers is divisible by 4. To find a counterexample, we need to find a pair of even integers whose sum is not divisible by 4.<br /><br />Let's examine each option:<br /><br />(A) 2 and 6: The sum is 8, which is divisible by 4.<br />(B) 3 and 7: Neither 3 nor 7 is an even integer, so this option is not valid.<br />(C) 4 and 4: The sum is 8, which is divisible by 4.<br />(D) 6 and 8: The sum is 14, which is not divisible by 4.<br />(E) 8 and 9: The sum is 17, which is not divisible by 4.<br /><br />Among the valid options, (D) 6 and 8 and (E) 8 and 9 both provide counterexamples to the statement. However, since the question asks for a single pair, we can choose either (D) or (E) as the correct answer.