Help me, was given a Mathematical problem to figure out, but the answers told me it was just demorgans law in c code.

Question

Was given this to figure out. He said its mathematical, no its not homework. More of one guy trying to prove he is smarter than me.

The code:

(!(a&&b)) == |!a||!b|  T
!(a||b) == !a&&!b

I think it might be some symbolic logic, but couldn't figure out from reading about symbolic mathematics from google searches. That is only my guess.

Answer 1

This is (almost) DeMorgan's laws written in C-language syntax (though other languages use the same syntax, too). Writing it a bit more tidily, it would be:

!(a && b) = (!a) || (!b)

!(a || b) = (!a) && (!b)

That's not exactly what you wrote, but I expect it's what you meant to write.

I don't know anything about symbolic logic notation, but in set-theoretic notation, the equivalent laws would be:

$$ (A \cap B)^c = A^c \cup B^c $$

$$ (A \cup B)^c = A^c \cap B^c $$

Or, in English (almost):

not(A and B) = (not A) or  (not B)
not(A or  B) = (not A) and (not B)

Answer 2

This is De Morgan's law. See here.