Question

1) Let X = {x, y} and list the four elements of the power set P(A). (The Power set is P(A) = { 0, (x), (y), (x, y)} ) Consider the operations + to be U, • to be n, and a complement to be set complement. Also, consider 1 to be X and 0 to be Not 0.
a) Explain why the description above defines a Boolean algebra.
b) Find two elements a, b in P(X) such that:
i. xy = 0,
ii. x =/ 0 and
iii. y =/ 0.