Discrete Mathematics and Combinatorics

Chapter 10

Posets, Lattices and Boolean Algebras

Learning Objectives

On completing this chapter, you should be able to:

• state the algebraic definition of a Boolean algebra

• solve problems using the algebraic properties of the elements of a Boolean algebra

• define a poset and find the maximum and minimum elements of subsets of posets when they exist

• find the supremum and infimum of subsets of posets when they exist

• define a lattice and identify lattices among posets

• define and verify distributive property for lattices

• define a sublattice

• state the definitions of a bounded lattice and a complete lattice

• identify bounded and complete lattices

• prove or disprove the existence of a compliment of an element in simple lattices

• state the lattice/order ...