Question

What is a counterexample for the conjecture?

Conjecture: The product of two positive numbers is greater than the sum of the two numbers.

A. 3 and 5
B. 2 and 2
C. A counterexample exists, but it is not shown above.
D. There is no counterexample. The conjecture is true.

Answer 1

The answer is B.

A conjecture is a conclusion formed from incomplete evidence. Since 2 and 2 do not create a bigger product than the sum, it provides as a counterexample.

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Answer 2

Consider options A and B:

A. The product of 3 and 5 is 15, the sum of 3 and 5 is 8.

The product of 3 and 5 is greater than the sum of 3 and 5, because 15>8. In this case the statement is true.

B. The product of 2 and 2 is 4, the sum of 2 and 2 is 4.

The product of 2 and 2 is not greater than the sum of 2 and 2, because 4=4. In this case the statement is false and this option is a counterexample for the conjecture.

Therefore, options C and D are not true, because you have counterexample and you know it.

Answer: correct choice is B.