# Venn

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• May 6th 2011, 12:09 PM
yorkey
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.
• May 6th 2011, 12:12 PM
Ackbeet
You're very welcome. I am a he, by the way, just fyi. (Wink)
• May 6th 2011, 03:56 PM
Deveno
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.
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