Translating English to Propositional Logic for NOR

Question

Having difficulty with translating English to propositional logic.

For example:

1. Cows eat grass (C), humans eat bricks (H).
2. Neither cows NOR humans eat bricks.
3. If children believe humans eat bricks (B), then humans eat bricks.

I understand that it would look like this for the first one:

1. C ∧ H

But having difficulty with the second one because I'm not sure how to translate it so that it's specific to just "bricks". It makes sense if it was "Neither cows eat grass nor humans eat bricks" because it would be

2. ¬(C ∨ H)

Also, I believe that the third one would be:

1. B → H

Could I please get some clarification on how to do the second one?

Thanks!!

Answer 1

For the second one, yes, you're absolutely right: we need to know how to symbolize that cows eat bricks. We know how to symbolize that cows eat grass, and that humans eat bricks, but the claim that cows eat bricks is neither of those. And if it was neither cows eat grass nor humans eat bricks then indeed it would be $\neg (C \lor B)$, you're right about that as well. You could equivalently do $\neg C \land \neg B$

For the third one, make sure you use $B$ and $H$ ... not sure where your $J$ and $W$ come from ....