# Question about sets

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• December 3rd 2011, 11:26 AM
Nombredor
Re: Question about sets
Quote:

Originally Posted by Plato
Correct. So the OP
Is incorrect.

OK, I see where I made a glitch. I was assuming that on a Venn diagram, the default way to represent A and B was ''partly separated'' and ''partly joined together'', but this isn't necessarily the case. When we only have a reunion and not an intersection, A and B don't have to be joined together at all, and the operation still works anyway.
• December 3rd 2011, 11:45 AM
Nombredor
Re: Question about sets
Attachment 22984

In this picture, how can we be sure that all possible combinations of 4 sets A-B-C-D are represented ?
• December 3rd 2011, 12:06 PM
Plato
Re: Question about sets
Quote:

Originally Posted by Nombredor
OK, I see where I made a glitch. I was assuming that on a Venn diagram, the default way to represent A and B was ''partly separated'' and ''partly joined together'', but this isn't necessarily the case. When we only have a reunion and not an intersection, A and B don't have to be joined together at all, and the operation still works anyway.

Venn diagrams are a wonderful way to see outcomes.
But they are a lousy way to prove anything.
\begin{align*}(A\cup B^c)\cap (A\cup B)&=A\cup (B^c\cap B)\\&=A\cup (\emptyset)\\&= A \end{align*}
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