Relations

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Malaysia SPM Additional Mathematics, Chapter 1, Function and Relation
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1 Relations
2 Domain, Codomain, Image, Object and Range
3 Type of Relation
4 Recommended Webpage

[edit] Relations

A relation connects elements in set A (domain) to elements in set B (codomain) according to the definition of the relation.

Relation between two sets can be represented by
(a) Arrow diagram
(b) Ordered pairs
(c) Cartesian graph

Example 1

The relation ‘is a factor of’ between set A = { 3, 4} and set B = {4, 6, 8} can be represented as below:

(a) Arrow diagram

(b) Ordered pairs

{(3, 6), (4, 4), (4, 8)}

[edit] Domain, Codomain, Image, Object and Range

In the relation between one set and another, the first set is known as the domain and the second set is known as the codomain.

Elements in the domain is called objects, whereas elements in the codomain mapped to the objects is called the image. Elements in the codomain not mapped to the objects are not the image.

All images in codomain can be written as a set known as range.

Example 2

The diagram above shows the relation between set A and set B. Find the domain, codomain and range of the relation.

Answer

The domain is {a, b}

The codomain is {p, q, r, s}

The range is {p, q, r}

[edit] Type of Relation

	Types of Relation	Diagram
1	One to One Relation In this relation, each object in the domain has only one image in the codomain.
2	One to Many Relation In this relation, one or more than one of the objects in the domain has more than one image in the codomain.
3	Many to One Relation In this relation, there are more than one objects in the domain that have the same image in the codomain.
4	Many to Many Relation In this relation, one or more than one of the objects in the domain has more than one image in the codomain, and there are more than one object in the domain that have the same image in the codomain.