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!
Best Answer
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.