## Department of Mathematics, 2004

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### REPRESENTASI RELASI BINER DALAM GRAPH DAN MATRIKS

Kurniawati Dwi Wahyuni

#### Abstract

ABSTRACT
In daily life, the relationship of objects are often used, for instance, to represent the relationship between student lecheries, parents and children and many more. In field of mathematics, it is also used to represent the relationship of numerals, functions, and others. In connection with many uses of relation concept bring out a thinking into view, how to represent binary relation into a questions especially in a set of ordered pairs.
Binary relation (relation) from set A to set B is subset from A?B, given a?A and b?B. There are some ways for representing the relation of set to be other forms such as digraph and matrix.
If A is a discrete set and R is a relation in A, so R can be represented in picture by the steps as follow : Draw a small circle for each element A and label the circle with corresponding in element A. these circle are called vertices. Draw a directed line that show edge from vertex aI to vertex aj , if and only if aI R aj. The resulting pictorial representation of R is called a directed graph or digraph of R.
Thus if R is a relation on A, the edges in the digraph of R correspond exactly to the pairs in R, and the vertices correspond exactly to the element of the set A.
Beside Graph, matrix is also one of the methods that can be used to represent binary relation in a set. A relation in a set with m element A can be represented into numerals shaped a ninety degree angle gruadangle that is flanked by angle brackets have m?m measurement or called by matrix. For example, R is binary relation in discrete set V = {v1, v2, ?, vm}, so R can be represented into Boolean matrix A have m?m ordo. upld by//1528.com

Keyword : Relasi Biner, Digraph, Matriks

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