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Chapter13Boolean Algebra

George Boole, 1815 - 1864
Figure13.0.1George Boole, 1815 - 1864
George Boole
George Boole wasn't idle a lot.
He churned out ideas on the spot,
Making marvellous use of
Expressions like AND, OR, and NOT
Andrew RobinsonThe Omnificent English Dictionary In Limerick Form

In this chapter we will develop a type of algebraic system, Boolean algebras, that is particularly important to computer scientists, as it is the mathematical foundation of computer design, or switching theory. The similarities of Boolean algebras and the algebra of sets and logic will be discussed, and we will discover properties of finite Boolean algebras.

In order to achieve these goals, we will recall the basic ideas of posets introduced in Chapter 6 and develop the concept of a lattice. The reader should view the development of the topics of this chapter as another example of an algebraic system. Hence, we expect to define first the elements in the system, next the operations on the elements, and then the common properties of the operations in the system.