Relation And Mapping

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Relation And Mapping

ORDERED PAIR
By an orders pair (a, b) we mean a pair of two number a and b, strictly in the order with an at the first place and b at the second places Clearly ordered pair (a, b) not equal ordered pair (b, a)

In an ordered pair (a, b), a is called the first component, and b is called the second component.
Note 1 Both the components of an ordered pair can be the same as (a, a),(2,2), etc.
Two ordered pairs (a, b) and (c, d) are equal if a =c and b=d.

Relations
Study the following sentences
Sita was the wife of Rama.
New Delhi is the capital of India
51 is greater than 34

All these sentences express the relationship between two objects.
Thus the word “relation” implies an association of two objects (people, numbers, ideas, etc.) according to some property possessed by them.

Definition: A relation is a set of ordered pairs. Any set of ordered pairs is, therefore, a relation. The set of first components of the ordered pairs is called the domain and the set of second components is called the range.

Roster Form: By describing a set of ordered pairs. For example, {(4,2),(9,3),(16,4),(25,5)}.In this relation, the second member is the square root of the first member.

Set builder Form: By standard description using a rule or formula in the for(x, y):–}, the blank to be replaced by the rule or condition.

Mapping
Let A=(Dhyan Chand, Anita Sood, R.Krishnan, Kapil Dev}
B{Cricket, Tennis,  Swimming, Hockey}
If we associate each player of an A with the corresponding sports of B, then we have
(Dhyan Chand, Hockey), (Anita Sood, Swimming),(R.Krishnan, Tennis)( and Kapil Dev, Cricket)
In mathematics, such an association between elements of set A and set B is called mapping from A to b.

Necessary Conditions For mapping

When the relation from A to b is represented in Roster form.
Every element of set A associates with a unique element of set B
No two ordered pairs of the relationship should have the same first component

When the relation from A and B represented by an arrow diagram
Each element of set A matches with unique elements of set B.
There should not be any elements in A that do not have its matching in B.