1. ## Re: Question about sets

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.

2. ## Re: Question about sets

In this picture, how can we be sure that all possible combinations of 4 sets A-B-C-D are represented ?

3. ## Re: Question about sets

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*}

Page 2 of 2 First 12