Posets, Lattices, and Boolean Algebra
This chapter looks at topics important to computer science and electrical engineering as well as mathematics. All of them are on the relational side of algebra—posets, lattices, and Boolean algebras. Continuing what Chapter 6 began by exploring equivalence relations, now various order relations are studied, but mainly partial orders. Types of lattices are considered, culminating in Boolean lattices. This leads into Boolean Algebra, which is important for logic and its physical realization in logic circuits. Boolean functions are next introduced, and their minterm representations are explored. The chapter concludes by looking at the standard techniques for simplifying Boolean functions—K-Maps and the Quine-McCluskey Method.