Sets and relations

Sets and relations:

Introduction about sets and relations:

A group of elements is called a set when the elements in the group are distinct. A characteristic of two objects is called Relation
.
Example of a Set:

• The collection of all natural numbers
• The collection of all equilateral triangles in a plane.

Let us learn more about sets and relations in this chapter.

A relation is a set of ordered pairs(x,y) , where the first component of the ordered pairs are the input values and the second component are the output values.

Set of all Input Values is known as Domain of the given Relation.

Similarly, set of all Output Values is known as Range of the given Relation.

Mathematically,

A relation R defined by ( , {(x,y):x }) ,is the set of ordered pairs of all Input Values (x) and all Output Values(y) such that each element x is related to the corresponding element y.

Here,

x=Domain of the Relation and

y=Range of the Relation

iff no values of x and y is repeated.

x is called Independent variable and y is called Dependent variable because its value depends on the x-value chosen.The most commonly asked question is how do we express a relation,we come across this question very frequently. Relation scan be represented in any of the following forms:-

(i) Roster form

This method is also known as Tabular method. In this method, a set is represented by writing all the elements of the set, separated by commas and are enclosed withinbrackets { }.

For e.g. D = {Sunday, Monday, Tuesday,, Wednesday, Thursday, Saturday}.

Lets take some examples to show the relation in various forms:-

(ii) Set builder form Set builder notation has the form {x : f(x)} (some write {x | f(x)}, using the vertical bar instead of the colon), denoting the set of all individuals in the universe of discourse satisfying the formula f(x), that is, the set whose members are every individual x such that f(x) is true.For e.g. is the set of all positive real numbers.

(iii) By tables

Table representation of the RelationInputOutputa3c2e9
(iv) Arrow diagram :-

(v) By graphs:-

Hope you like the above example of Sets and Relations. .Please leave your comments, if you have any doubts.