11M02
Relations and Functions
Relations
11M02.1
Cartesian Product
11M02.1 – Relations and Functions
Learning Objectives
Ordered Pair
Cartesian Product of Sets
Ordered Triplet
11M02.1
CV 1
Ordered Pairs and Ordered Triplets
Ordered Pair
Sumit
Amol
Radha
Singh
Kumar
(Sumit, Kumar)
(Radha, Singh)
(Singh, Radha)
Ex.
Sol.
Ordered pairs are :
1
2
3
5
6
7
Ordered Pair
Sumit
Amol
Radha
Singh
Kumar
11M02.1�CV 2�Difference Between Set and Ordered Pair
Sets
Ordered Pairs
Ordered Triplet
11M02.1�CV 3�Equality of Ordered Pairs
Ex.
Sol.
Given ,
11M02.1
PSV 1
Sol.
Given Ordered Pair are equal .
(NCERT - Ex 2.1 – Q1)
11M02.1
CV 4
Cartesian Product
Blue
Red
Black
Pen��Pencil
Cartesian Product = set of all possible ordered pairs
(Blue,Pen)
(Blue,Pencil)
(Red,Pen)
(Red,Pencil)
(Black,Pen)
(Black,Pencil)
Blue
Red
Black
Pen��Pencil
Cartesian Product = set of all possible ordered pairs
(Pen, Blue)
(Blue,Pencil)
(Pen, Red)
(Red,Pencil)
(Pen, Black)
(Black,Pencil)
Blue
Red
Black
Pen��Pencil
Cartesian Product = set of all possible ordered pairs
Ex.
Sol.
1
2
3
5
6
7
11M02.1
PSV 2
Sol.
7
8
5
4
2
5
4
2
7
8
(NCERT - Ex 2.1 – Q3)
ConcepTest 1
Ready For Challenge
Q.
(NCERT - Ex 2.1 – Q6)
Pause the video
(Time Duration: 4 Minutes)
Q.
(NCERT - Ex 2.1 – Q6)
Sol.
11M02.1
CV 5
Important Points about Cartesian Product
Ordered Triplet
Ex.
Sol.
-1
1
-1
1
-1
1
(NCERT - Ex 2.1 – Q5)
ConcepTest 2
Ready For Challenge
Q.
(NCERT - Ex 2.1 – Q10)
Pause the video
(Time Duration: 4 Minutes)
Q.
(NCERT - Ex 2.1 – Q10)
Sol.
11M02.2
Relations
11M02.1 – Relations
Learning Objectives
What is Relations
How to represent Relations
11M02.2
CV 1
What is Relation
Ex.
1
2
3
4
5
Sol.
11M02.2
PSV 1
Q.
Sol.
(NCERT - Ex 2.2 – Q1)
11M02.2
CV 2
Important Points and Representation of Relations
In set-builder form
In roster form
9
16
25
3
4
5
Relation - elements of A are the square of the elements of B.
Representation of Relation is possible using two ways
1. Algebraical Representation
2. Visual Representation
Arrow Diagram
Ex.
Representation-
Arrow Diagram
Sol.
Representation of Relation is possible using two ways
1. Algebraical Representation
2. Visual Representation
Arrow Diagram
We know,
No. of Relations
11M02.2
PSV 2
Sol.
(NCERT - Ex 2.2 – Q8)
No. of Relations
We know,
No. of Relations =
ConcepTest
Ready For Challenge
(NCERT - Ex 2.2 – Q6)
Pause the video
(Time Duration: 4 Minutes)
Sol.
(NCERT - Ex 2.2 – Q6)
Roster Form
11M02.3
Functions
11M02.3 – Functions
Learning Objectives
What is Functions
How to represent Functions and Types
Algebra of Real Functions
Graph of Real Functions
11M02.3
CV 1
What is Functions
Those two specific rules are:-
Only if it follows two specific rules:-
Rule - 1
Rule - 2
Not a Function
Rule - 1
Rule - 2
Is a Function
Functions
Which have two specific rules:-
9
16
25
3
4
5
Domain
9
16
25
3
2
4
5
Co-domain
Range
Ex.
Sol.
11M02.3
CV 2
How to represent Functions and Types
Representation of function
Dependent
Independent
Range
Domain
Sol.
Ex.
Types of function
Identity functions
Constant functions
Polynomial functions
Rational functions
Modulus functions
Signum functions
Greatest integer functions
Definition
Domain
Range
Graph
- Straight line
- Passes through the origin
Definition
Domain
Range
Graph
- Straight line
Definition
Domain
Range
Ex.
Definition
Domain
Range
Ex.
Definition
Domain
Range
Ex.
Definition
Domain
Range
Definition
Domain
Range
Definition
Domain
Range
Definition
Domain
Range
11M02.3
CV 2
Algebra of Real Functions
Algebra of real function
Example :
Subtraction of a real function from another real function
Example :
Multiplication by a scaler
Example :
Multiplication of two real functions
Also called pointwise multiplication.
Example :
Quotient of two real functions.
Example :
Sister
Brother
Ex.
Sol.
Ordered pairs are :
1
2
3
5
6
7
Ordered Pair
It consist of two elements or object in fixed order.
Ex.
Sol.
1
2
3
5
6
7
Ordered pairs are :
Ordered Triplet
A relation may be represented algebraically.
Ex.
a
b
c
d
e
Ex.
Either by Roster Form method or by the Set Builder Method
Functions
Which have two specific rules:-
Examples : Define after domain, Co-domain, Range.
Image and Pre-image