However some of the areas might simply be different names for the same area and therefore not enjoy a separate existence. Consider for example 3 concentric circles A, B and C of increasing radius. Then areas W, Y and Z are all the same area. Nonetheless they all exist!
All three must exist. If A, B, and C overlap then A and B overlap etc.
Z is a subset of W.
Z is a subset of X.
Z is a subset of Y.
Well... are W,X, & Y necessarily at least partially exclusive?
Are the three circles of the same diameter?
(As you state it, the three circles might be concentric y'know.)
If they are exclusive, then - If Z exists then, since A.B.& C share
at least some small common area and thus W X &Y must exist.
Z can only exist if W, X and Y exists. Therefore if you say Z exists then W, X, and Y should also exists.!
Consider the trivial solution:
Z = (A + B + C), and A,B, and C are non-zero.
If Z exists, (A + B), (B + C), and (A + C) exist.
Proof format escapes me.
Who knows the answer?
Consider 3 circles: A, B and C.
Where A and B overlap, it creates area W.
Where B and C overlap, it creates area X.
Where A and C overlap, it creates area Y.
Where A, B and C overlap, it creates area Z.
If area Z exists, must area W, X or Y exist? If so, which ones?
