May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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8-2 Discrete Mathematical Structures
8.1 INTRODUCTION
The concept of relation discussed in Chapter 2 will now be associated with the idea of ordering
the elements of a set. This will lead to the concept of linear ordering and total ordering, which is
of great importance in mathematics and computer science. It gives rise to the concept of lattice,
which will be discussed in this chapter.
8.2 PARTIALLY ORDERED SET
A relation R on a set A is called a partial order relation if R is reflexive, antisymmetric and
transitive. The set A together with partial order relation R is called a partially ordered set or
simply a POSET and is denoted by (A, ≤ ), the symbol ≤ is used for partial order relation.
Example 1 Let P(S) be the collection of all subsets ...
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