Question

Which statement is the following a counterexample for?

2 ∙ 11 = 22
A. If you multiply two numbers greater than 5, then their product is greater than 25. B. If the product of two numbers is even, then both numbers must be even.
C. If x ∙ y = 1, then x or y must equal 1.
D. If two times a number is greater than 16, then the number must be greater than 9.

Answer 1

counter example of 2 * 11 = 22 ....

B. If the product of 2 numbers is even, then both numbers must be even.

Answer 2

The correct answer is option B.

Here is why. This sentence is a product of two numbers. equals a third one.

2 *.11 = 22

and there is only one even factor (which is 2). The other one is an odd number: 11.

Though not all factors are even, the product still is, which makes this sentence

2 * 11 = 22

a counterexample for this statement:

"If the product of two numbers are even, then both numbers must be even too".

That is not true, as 2 * 11 is a product with an odd number as a factor, and the result is an even number the same way.

Answer: option B

I hope this helps. =)