SOLUTION: Suppose you have a Venn diagram showing three sets. Call the sets A, B, and C. How many regions of the Venn diagram correspond to elements that are part of set A? Why so many?

 
A is made up of 4 regions d, e, f, and g

Why 4?  Because 
1. d is the part of A which is not part of B or C,
2. e is the part of A which is also part of B but not part of C.
3. g is the part of A which is also part of C but not part of B.
4. f is the part of A which is also part of B and C.

That's all you asked but you need to know the
following as well:

B is made up of 4 regions e, f, h, and i
C is made up of 4 regions f, g, i, and j

Region d is part of A but is not part of B or C
Region h is part of B but is not part of A or C
Region j is part of C but is not part of A or B

Region e is part of A and B, but is not part of C
Region g is part of A and C, but is not part of B
Region i is part of B and C, but is not part of A

Region f is part of A, part of B, and part of C

Region k is not part of any of A, B or C.




Edwin