Relations ( JEE Mains)

Relations

 Scope of Relations in JEE :- Sets and Relations comes together in JEE mains and its     not included in JEE Advanced syllabus. but its a fundamental topic to start with the     preparation of JEE.

 What is Relations(Briefly Described)?                                                       

This topic “Relations and Functions” is a foundation or fundamental of algebra in mathematics. Relations and functions are two different words having different meaning mathematically. Many us you might be confused in their difference. We shall study both these concepts in detail here.

Same as the relations which we have in our daily life, a kind of relations also exists in algebra. In daily life, relations are like brother and sister, friends, student and teacher and many more. In mathematics also we see some relations like a line is parallel or perpendicular to another, any one variable is greater or less than the another variable. Any Set A is subset of B, all these are examples of relations.

One thing which we see in common while studying relations, that it required two different objects to link two different objects via relations.

For Example

Consider a set A containing elements as {1, 2, 3} and set B contains elements as {2, 4, 6}.

Then the relation between Set A and B from A to B will be set of any combinations from Set A to set B.



From the above diagram, we can see that Relation from A to B i.e. R will be set of {(1,4). (1,2), (3,4), (3,2)}. This relation is a subset of the Cartesian product of two sets A X B.

Let’s take another example where, set A = {1, 2, 3} and set B = {1, 2, 3, 4, 5, 6, 7, 8, 9}.

If the Relation between A and B is as: elements of B is the squares of elements of set A, then the relation is written in the form of sets as:

R  = {(a,b): where b is square of a and a ∈ A & b ∈ B}

Then R = {(1,1), (2,4), (3,9)}

Same as sets, relation may also be represented algebraically either by the Roster method or by the Set-builder method.

Relation can also be defined as a linear operation which establishes relationship between the element’s of two set’s according to some definite rule of relationship.

For complete information:-I m providing the link to my notes which are more than sufficient for JEE mains as well as for Boards :- Relations