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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

  1. ¬(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!!

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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 ....

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  • $\begingroup$ Still don't understand how to isolate it so that it's "Neither cows nor humans eat bricks" because wouldn't: ¬C∧¬B mean "Neither cows eat grass nor humans eat bricks"? EDIT: Wait, I think you're telling me to create another symbol that tells us that "Cows eat bricks" (E), right? $\endgroup$ – Kammy Mar 1 '18 at 2:06
  • $\begingroup$ "Neither cows nor humans eat bricks" is "Both cows and humans do not eat bricks." @Kammy So yes, create a new symol for cows eat bricks" $\endgroup$ – Graham Kemp Mar 1 '18 at 2:09
  • $\begingroup$ @Kammy yes, you need a new symbol ... can you just pick your own symbol, or are they given to you? $\endgroup$ – Bram28 Mar 1 '18 at 2:11
  • $\begingroup$ I can pick my own but I wasn't sure if there was different way to do it without creating another symbol. Is there no other way to isolate the term "Cows eat" and make it work with "nor humans eat bricks"? If I do create a new symbol, would the statement then be: 2. ¬(E ∧ W) $\endgroup$ – Kammy Mar 1 '18 at 2:23
  • $\begingroup$ @Kammy You definitely don't want to use something that represents just 'cows eat', because that's not what is being used in the English sentence. And 'nor humans eat bricks' isn't even a sentence; the 'nor' is a logical connective that goes between sentences. So, stick to 'cows eat bricks' and 'humans eat bricks'. Picking $E$ for the former, and using $H$ for the latter, you get $\neg (E \lor H)$ $\endgroup$ – Bram28 Mar 1 '18 at 12:37

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