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Discrete Mathematics and Combinatorics by T. Sengadir

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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 ...

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