Summary Class 11 Maths JEE Brilliant Pala Notes - Relations and Functions

RELATION & FUNCTION



Ordered pairs
(a,b) is called ordered pair

  a, b    b, a 
  a, b    c, d   a  c & b  d
Cartesian product of sets (cross product)
If A and B are two sets then the cartesian product is given

A  B   x, y  : x  A, y  B

B  A   x, y  : x  B, y  A

eg: A  1, 23 , B  3, 4

A  B  1,3 , 1, 4  ,  2,3 ,  2, 4  ,  3,3  ,  3, 4 

B  A   3,1 ,  3, 2  ,  3,3 ,  4,1 ,  4, 2  ,  4,3

Thus A  B  B  A




1

, Arrow Diagram representation




Now A  A   x, y  x  A, y  A


Here A  A  1,1 , 1, 2  , 1,3 ,  2,1 ,  2, 2  ,  2,3 ,  3,1 ,  3, 2  ,  3,3 
Important Results

If n  A   m & n  B   n

Then n  A  B   n  B  A   mn

& n  A  A   m2

NCERT Ex.1: If  x  1, y  2    3,1 find x & y

x  1  3, y  2  1

x  2, y  3

NCERT Ex.4: If A  1, 2 find A  A  A

A  A  A  1,1,1 , 1,1, 2  , 1, 2,1 , 1, 2, 2  ,  2,1,1 ,  2,1, 2  ,  2, 2,1 ,  2, 2, 2 

NCERT Ex.6:If A  B   p,q  ,  p, r  ,  m, q  ,  m, r 
Then find sets A & B

A  p, m ; Bq, r




2

, NCERT Ex.2.1 Qn.7. If A  1, 2 , B  1, 2,3, 4 , C  4, 5

Then find  i  A   B  C 

(ii)  A  B   A  C 

 iii  A   B  C 
 iv  A  B   A  C 
Important Results

(1) A   B  C    A  B    A  C 

(2) A   B  C    A  B    A  C 

(3) A  B   then either A or B is 

2
(4) n  A  B    B  A     n  A  B  

Relations: A Relation R from a non empty set A to a non empty set B is a subset of A×B or Any subset
of A×B is a relation from set A to set B. If R is a relation from set A to set B we denote it
as R : A  B . Any subset of A×A is called a relation from A  A or relation on A.
Domain , Range & codomain of a relation.
Let R : A  B be a relation from A  B . Then set of all first elements of ordered pairs of
R is called
Domain of R
The set of all second elements of ordered pairs of R is called
Range of R
Set B is called co-domain of ordered pairs of R is called

ex: Let A  1, 2,3, 4,5 B  3,5, 7,9

Let R : A  B be a relation by R   x, y  : x  A, y  B, y  x  2
Now R in Roster form is given by

R  1,3 ,  3,5  ,  5, 7 

Domain = 1, 3,5




3