Question

Which of the following is a counterexample for this conditional statement?

If the number is even, then it is 2 times an odd number.
(A) 7
(B) 4
(C) 14
(D) 6

Answer 1

Option (B) 4 serves as a counterexample to the statement because it is an even number that is not 2 times an odd number, but 2 times another even number.

Step-by-step explanation:

The question asks for a counterexample to the conditional statement, "If the number is even, then it is 2 times an odd number." A counterexample is an example that disproves the statement by showing that even though the number is even, it is not 2 times an odd number. Looking at the options given:

• (A) 7 is an odd number and thus not relevant to the statement about even numbers.
• (B) 4 is 2 times 2, which is an even number, not an odd number, so this is the counterexample.
• (C) 14 is 2 times 7, and since 7 is an odd number, it does not serve as a counterexample.
• (D) 6 is 2 times 3, and since 3 is an odd number, it does not serve as a counterexample.

Therefore, the correct answer is (B) 4.