Originally Posted by

**chaosier** I am given a problem asking me to identify pairwise disjoint sets that satisfy some property, unfortunately I do not know how I would construct them.

I'm given sets Y1, Y2, ... and I'm asked to identify pairwise disjoint sets Z1, Z2, ... that satisfy the property (UNION Zi for i = 1 to n) = (UNION Yi for i = 1 to n).

I know that if Z1, Z2, ... are pairwise disjoint sets, then (UNION Zi for i = 1 to n) = sum{from i = 1 to n}(Zi).

sum{from i = 1 to n}(Zi) = (UNION Yi for i = 1 to n).