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
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, 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 ; Bq, r
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, 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
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