Relations and Functions Solutions and Shortcuts
Relations and Functions Examples  Page 2
Relations and Functions Questions  Page 4
Relations and Functions Video Lecture  Page 5
Consider the two sets P = {a,b,c} and Q = {Ali, Bhanu, Binoy, Chandra, Divya}.
The cartesian product of P and Q has 15 ordered pairs which can be listed as P × Q = {(a, Ali),(a,Bhanu), (a, Binoy), ...,
(c, Divya)}. We can now obtain a subset of P × Q by introducing a relation R between the first element x and the
second element y of each ordered pair ( x , y) as R= { (x,y) : x is the first letter of the name .Then R = {(a, Ali), (b, Bhanu), (b, Binoy), (c, Chandra)}A visual representation of this relation R (called an arrow diagram) is shown in Fig 2.4
Definition: A relation R from a nonempty set A to a nonempty set B is a subset of the cartesian product A×B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A×B. The second element is called the image of the first element. or
The set of all first elements of the ordered pairs in a relation R from a set A to a set B is called the domain
of the relation R.. or
Definition: The set of all second elements in a relation R from a set A to a set B is called the range of the relation R. The whole set B is called the codomain of the relation R. Note that range ⊆ codomain.
Note:
 A relation may be represented algebraically either by the Roster method or by the Setbuilder method.
 An arrow diagram is a visual representation of a relation.
Important Point: The total number of relations can be define from a set A to a set B is the number of possible subset of a A*B. If n(A) = P and n (B) = q , then n(A*B) = pq and the total number of relation is 2pq
Latest Jobs

 Type
 Job Notification
 Job
 IBPS Recruitment Specialist Officers 1163 Vacancies  Last Date 26112019
 Location
 Anywhere
 Date Posted
 20 Nov 2019

 Type
 Job Notification
 Job
 CISF Recruitment for 300 HEAD CONSTABLE  SPORTS QUOTA  Last Date 17122019
 Location
 Anywhere
 Date Posted
 19 Nov 2019

 Type
 Job Notification
 Job
 IOCL Invites Application for 1542 Apprentice  Last Date 15112019
 Location
 Anywhere
 Date Posted
 5 Nov 2019

 Type
 Job Notification
 Job
 SAIL Bhilai Recruitment of Operator cum Technician, Nurse, Fire Station Officer, and more  Last Date 15112019
 Location
 Vaishali NagarChhattisgarh, India
 Date Posted
 5 Nov 2019

 Type
 Job Notification
 Job
 Naval Ship Repair Yard, Karnataka Recruitment of 145 ITI qualified.  Last Date 01122019
 Location
 KarwarKarnataka, India
 Date Posted
 5 Nov 2019

 Type
 Job Notification
 Job
 IIT Dhanbad 191 Recruitment Engineers, Staff Nurse and others  Last Date 14122019
 Location
 DhanbadJharkhand, India
 Date Posted
 5 Nov 2019

 Type
 Job Notification
 Job
 INDIAN Bank Recruitment of 115 Security Guard cum Peon – Last Date 08112019
 Location
 Anywhere
 Date Posted
 28 Oct 2019

 Type
 Job Notification
 Job
 AIIMS Rishikesh 184 Recruitment Staff Nurse, Assistant Nursing Superintendent – Last Date 30112019
 Location
 RishikeshUttarakhand, India
 Date Posted
 28 Oct 2019

 Type
 Job Notification
 Job
 Cement Corporation of India Recruitment of 60 Artisan Trainees  Last Date  25102019
 Location
 Anywhere
 Date Posted
 25 Oct 2019

 Type
 Job Notification
 Job
 MFL Recruitment of 93 Engineering, Management Trainees, Assistant Trainees  Last Date 25102019
 Location
 ChennaiTamil Nadu, India
 Date Posted
 25 Oct 2019