elementary-set-theory
So Given that Set A and B are disjoint, then A intersection C and B intersection C are also disjoint.
Now I'm having trouble figuring out how to exactly draw That A intersection C and B intersection C are also disjoint. Would I just draw Set C in the middle of Set A & B and then A intersects with B and Set C intersects with B?
The numbers in the diagram indicate how many times the given formula counts that particular portion of the Venn Diagram. In the first picture, for example, an element in the intersection of A, B, and C will be counted 3 times. Each term of the inclusion-exclusion formula gradually refines these numbers until each portion of the Venn Diagram is counted exactly once.
For each pair in B you have to take m in {1,2,3} and n in {1,2,3,4}. In this case you have to make sure that m>n, so, for example, an element of B could be (2,1), because 2 is in {1,2,3} and 1 in {1,2,3,4} and 2>1.
Best Answer
I think you pretty much have it. The diagram would look something like this: