# Which one of the following pairs could be the two nominees for councillor?

on June 13, 2020

Am I missing a rule?

I've gone back over this question a few times and I keep finding that answer choices A, B, and C all work. Am I making a mistake with the rules or missing something?

Shunhe on June 14, 2020

Hi @kalinwoodward,

Thanks for the question! So let’s take a look at (A) and (C) and find out why they’re wrong. (B) is the right answer, so it’s good that it works!

(A) is wrong for a pretty simple reason. Take a look at the first rule, which tells us that if F is a nominee, then G can’t be a nominee. So trivially, F and G can’t both be nominees for councillor for this reason.

Now on to (C), which has G and H both being councillors. If G and H are both councillors, then that means that F is not picked. Why? Because of the contrapositive of the first rule.

F—> ~G

G —> ~F

If G is picked, then F can’t be picked, because if F were picked, G wouldn’t have been picked. So now we know that F can’t be picked. We also know that H is a councillor by hypothesis. But who does that leave to be treasurer? No one, because the treasurer must be F or H, but we made H a councillor, and F can’t be picked.

Hope this helps! Feel free to ask any other questions that you might have.