July 2010
Intermediate to advanced
576 pages
13h 3m
English
Content preview from Discrete Mathematics
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6
Lattices
A lattice is a special kind of an ordered set with two binary operations. Lattice structures are used in computing and mathematical applications.
6.1 LATTICE
Definition 6.1
A lattice is a partially ordered set (L, ≤) in which every subset {a, b} consisting of two elements has a least upper bound and a greatest lower bound.
We denote LUB({a, b}) by a ∨ b and call it join or sum of a and b. Similarly, we denote GLB ({a, b}) by a ∧ b and call it meet or product of a and b.
Other symbols used are
LUB: ⊕, +, ∪,
GLB: *, ·, ∩.
Thus Lattice is a mathematical structure with two binary operations, join and meet.
A totally ordered set is obviously a lattice but not all partially ordered sets are lattices.
EXAMPLE 6.1
Let A be any set and ...
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