Let A = {a, b} and list the four elements of the power set P (A). We consider the operations + to be ∪, · to be ∩, and complement to be set complement. Consider 1 to be A and 0 to be ∅.

Question

Let A = {a, b} and list the four elements of the power set P (A). We consider the operations + to be ∪, · to be ∩, and complement to be set complement. Consider 1 to be A and 0 to be ∅.
a. Explain why the description above defines a Boolean algebra.
b. Findtwoelementsx,yinP(A)suchthatxy=0,x̸=0andy̸=0.