Response to the following problem:
Denote by P(E) the set of all subsets of a non-empty set E, i.e., the power set of E. The operations ∪, ∩, are the operations of the union, intersection, and complement in the set theory. Show that {P(E),∪,∩, , ∅, E}, where ∅ is the empty set, forms a Boolean algebra.
Make sure you use enough details to support your answer.