Show the following for any two sets A and B.
a. ℘(A) ∪ ℘(B) ⊆ ℘(A ∪ B).
b. Is ℘(A) ∪ ℘(B) = ℘(A ∪ B)?
Either provide a proof to show that this is true or provide a counterexample to show that this is false.