How many Subsets without intersection exist in a Set with n elements?

Answer 1

See http://mathworld.wolfram.com/BellNumber.html for definition and see http://www.research.att.com/~njas/sequences/A000110 for values. FYI

Answer 2

n

Each element taken alone has no intersection with the other elements (not, of course counting itself, in which case the answer is trivial ---zero).

Each individual element is a proper subset.

Done.

Answer 3

The answer is 2^n=C(n,0)+C(n,1)+C(n,2)+.....+C(n.n). END!!