Question

What is a counterexample for the conjecture?

Conjecture: Any number that is divisible by 4 is also divisible by 8.

Choices:
o 24
o 40
o 12
o 26

I know that 24 and 40 are both divisible by 4 and 8.
I also know that 12 is not divisible by 8, but is divisible by 4. However, 26 is not divisibly by 4 and 8.
I think the correct answer is 12, but am I correct? Are they looking for 26 instead?

Answer 1

Any number that is divisible by 4 is also divisible by 8.

to show that this is false, you have to show a number that is divisible by 4 but not 8

26 is not a good choice because 4 does not divided it. The conjecture says if div by 4, then 8. It is not div by 4, so the conjecture does not apply.

you need a number div by 4, but fails for div by 8 to show the conjecture is hogwash.

Answer 2

Okay, so I was correct when I was thinking that 12 was the answer. Thanks!