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1
Introductory Discrete Mathematics
Show that the relation R on Z defined by the set {(a. b) : a = b (mod m)} is an
equivalence relation. This relation is called the congruence modulo m relation on
the set of integers. The equivalence classes of this relation are called
congruence ...
2
Foundations of Discrete Mathematics
10 Let R! and R2 be two equivalence relations on a set ;V. Prove that RiftR* is
also an equivalence relation on X. Generalise to the intersection of more than two
equivalence relations. Show by an example, however, that the union of two ...
3
A Beginner’s Guide to Discrete Mathematics
The obvious equivalence relation is equality, on any set. In sets other than
number sets, equal objects are often called "equal in all respects." More
generally, an equivalence relation can be considered as a statement that two
objects are ...
4
Discrete Structures, Logic, and Computability
Thoroughly updated, the new Third Edition of Discrete Structures, Logic, and Computability introduces beginning computer science and computer engineering students to the fundamental techniques and ideas used by computer scientists today, ...
5
Handbook of Discrete and Combinatorial Mathematics
Definitions: An equivalence relation on A is a binary relation on A that is reflexive,
symmetric, and transitive. If R is an equivalence relation on A, the equivalence
class of o C A is the set R[a] = {b E A | aRb}. When it is clear from context which ...
in a set is an equivalence relation if it is reflexive, symmetric, and transitive. The
smallest equivalence relation in a set X is the relation of equality in X; the largest
equivalence relation in X is X X X. There is an intimate connection between ...
7
The Mathematics Dictionary
E.g., if one says that a is equivalent to b if a - b is a rational number, this is an
equivalence relation for the real numbers; the equivalence class which contains
a number a is then the class which contains all numbers which can be obtained
by ...
8
Fuzzy Logic with Engineering Applications
FIGURE 3.10 Five-vertex graph of equivalence relation (reflexive, symmetric,
transitive) in Example 3.10. (diagonal elements equal unity) simply indicates that
a city is totally related to itself. The property of symmetry might represent proximity
: ...
9
Contemporary Abstract Algebra
This mechanism is an equivalence relation. Definition Equivalence Relation An
equivalence relation on a set S is a set R of ordered pairs of elements of S such
that 1. (a, a) E R for all a E S (reflexive property). 2. (a, b) E R implies (b, a) E R ...
As the name suggests, homotopy equivalence is an equivalence relation on any
set of spaces. In order to prove this, we first prove that homotopy is an
equivalence relation on the set of all maps between two given spaces.
Proposition 2.2.7 ...
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Nkrumah Did Not Force His Views On African Leaders 7
There is thus a clear equivalence relation between regional bodies and state bureaucracy. Likewise, one cannot deal with critical questions ... «GhanaWeb, Cze 15»
An Advance in Mesoscale Graph Theory with implications for Whole …
For example, Helge Aufderheide, Lars Rudolf and Thilo Gross examined food web graphs and defined an equivalence relation over these ... «h+ Magazine, Kwi 13»
Putting Things In Order
... always false) and symmetric (because "and" is commutative), and therefore that this requirement makes "unordered" an equivalence relation. «Dr. Dobb's, Cze 11»
Alternative Axioms: NBG Set Theory
Well, you can at least speak metamathematically about classes, as formulas with parameters under an equivalence relation. A lot of theorems ... «ScienceBlogs, Cze 07»
