2

I have a question on sentential logic. I have the following sentence that needs to be translated:

"Pudding is neither good nor fattening."

G=Pudding is good. F=Pudding is fattening.

I gave the following answer : not G and not F But it seems that the real answer is : not(G or F)

Wouldn't the two be equivalent ? If we consider "or" to mean both G and F,(In this case) then we are really saying the same thing. Aren't we ? By the way, my knowledge of logic is minimal, so try to talk in a way with someone who's only learning. Thank yoU!

  • They are equivalent, but that doesn't mean they are both translations of the same sentence. – Git Gud Jun 07 '14 at 16:35
  • So, my answers would be no problem? –  Jun 07 '14 at 16:36
  • I'm hinting that you're answer might not be correct. Consider the statements Every creature with a heart is mortal and Every creature with a kidney is mortal. Would you translate them in the same way? Probably not, yet, since every creature has a kidney if, and only if, it has a heart, they are equivalent. – Git Gud Jun 07 '14 at 16:40
  • In any case, I think that if one of the translations is better than the other, yours is better. Your answer is correct. – Git Gud Jun 07 '14 at 16:46
  • ok, thank you for your answers ! –  Jun 07 '14 at 17:59

1 Answers1

3

They are equivalent; that is De Morgan's Law, which states that \begin{equation*} \neg (A \vee B )=\neg A \wedge \neg B \end{equation*} where $\vee$ is or, $\wedge$ is and, and $\neg$ is not.

Hayden
  • 16,737