I'm currently studying discrete mathematics and am having some difficulties with understanding boolean algebra. To be specific, I'm stuck on the following 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 ∅.

 1. Explain why the description above defines a Boolean algebra
 2.  Find two elements x, y in P(A) such that xy = 0, x != 0 and y != 0.

```

Starting with the power set 

```
P(A) = {∅, {a},{b},{a,b}}

```

How would I go about finding the elements of x & y to satisfy part two of the question using algebraic axioms? Also, for explaining how the above defines a boolean algebra, do you think it would suffice to simply mention how there are two binary operations and a set associated with the boolean algebra? 
Any help is appreciated, thanks!