Let A a b and list the four elements of the power set P A W

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,x=0andy=0.

Solution

a U b = a + b

a b = a · b

A = 1

= 0

The above table shows that a + b is a boolean algebra a OR b.

The above table shows that a · b is a boolean algebra a AND b.

Sorry I am not able to follow what your second question is. Is it x compliment = 0 & y compliment = 0?