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 following property.
I know that if Z1, Z2, ... are pairwise disjoint sets, then
Substituting this into the property we get:
What should be the next step?
How does this revelation help construct the pairwise disjoint sets and how does it relate to the property?
EDIT: Rephrased question