In assume that B is a Boolean algebra with

Chapter 6, Problem 5E

(choose chapter or problem)

Problem 5E

In assume that B is a Boolean algebra with operations + and ∙. Prove each statement without using any parts of Theorem unless they have already been proved. You may use any part of the definition of a Boolean algebra and the results of previous exercises, however.

Theorem Double Complement Law

For all elements a in a Boolean algebra B,  = a.

Proof:

Suppose B is a Boolean algebra and a is any element of B. Then

and

Thus a satisfies the two equations with respect to  that are satisfied by the complement of . From the fact that the complement of a is unique, we conclude that  = a.

Exercise

For all a and b in B, (a ∙ b) + a = a.