system
Given the following post, respond as if you're commenting on Reddit:
human
Is De Morgan's Theorem true for more than two things?

De Morgan's Theorem states that (not A) and (not B) is equal to not (A or B) (or, if you prefer that, A nor B), and vice versa.

My question is, is this also true for more than two things? For example, does (not A) or (not B) or (not C) equal not (A and B and C)?

Tagging this as maths because I reckon boolean algebra counts as maths!
gpt
Yes. You can show this directly via truth tables, but it is nicer to show this for three objects based on the result for two objects.  We use the associativity of AND and the associativity of OR (which is important, as otherwise something like  "A and B and C"  which you reference above has no meaning without parentheses).  Here's how you go from two to three:

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