I will notate & for "and" and v for "or"

A: I got X
B: I went to school.

~(A v B) = Neither I got X nor did I go to school.

which is equivalent to ~A & ~B = I did not get X and I did not go to school.

But what I have trouble with is

~A v ~B is I did not get X or I did not go to school.

which is equivalent to ~(A & B), but I do not know how to translate ~(A & B) into an English sentence.

Can anyone help me?

Also, what is the difference between Both I love 1 and I love 2 and I love both 1 and 2?

Are both sentences equal to A & B ?

  • 1
    & and ^ have the same meaning as conjunction in all notations I know. v means disjunction. I've edited for that purpose. – virmaior Sep 24 '14 at 8:58

~(A & B) is It is not the case that I both got X and went to school. You would rarely hear a sentence like this in natural English, which is why it is hard to translate.

Both of your sentences could be expressed by A & B in a simple logic such as the one you're using. If you were working with a predicate logic, the first would be L(A) & L(B), the second would be L(A & B).

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.