Thread: Venn

Thanks for your effort and patience, sir (or mam)! I think I've got it now, I'll just do some more examples to get it drilled into my head.

You're very welcome. I am a he, by the way, just fyi.

i think you want to get away from saying things like: "everything shaded but B".

the reason is, that usually, A and B are part of some larger collection, so "everything but B" isn't the same as "A", or even "A-B".

you wind up with two sets:

A∩B, and A∩B'.

note that both of these sets have part of A in them (well, hopefully. it could happen that B is so far away from A that there is no overlap, or that A is entirely inside B, so that there is no overlap between A and "not-B").

so one set is the part of A that overlaps with B, and the other set is the part of A that overlaps with everything else BUT B. put these two parts of A together, and you get A.

there is a distributive law of U and ∩ that applies here:

(A∩B)U(A∩B') = A∩(BUB').

but BUB' is "everything", sometimes called the "universe of discourse", or the "containing set" (in a Venn diagram, the rectangle containing the overlapping circles).

and the intersection of A with "everything", is just A.