Class 12 Maths - MP
Relations and Functions
The 'Relations and Functions' chapter in Class 12 Mathematics builds directly upon your Class 11 foundations, taking your understanding of sets to a much deeper and more abstract level. For MPBSE board exams, mastering this chapter is essential because it introduces fundamental ideas like types of relations (reflexive, symmetric, transitive, equivalence) and types of functions (one-one, onto, bijective). These concepts not only fetch direct marks in board examinations but also form the absolute backbone for advanced calculus topics like inverse trigonometric functions and calculus. Scoring well here requires precision in writing formal mathematical proofs.
Start Learning FreeKey Concepts
Empty and Universal Relations
An empty relation has no elements of set A related to itself, while a universal relation relates every element of set A to every element of A.
Equivalence Relation
A relation is called an equivalence relation if it is simultaneously reflexive, symmetric, and transitive.
One-One (Injective) Function
A function f from A to B is one-one if distinct elements of A have distinct images in B, meaning f(x1) = f(x2) implies x1 = x2.
Onto (Surjective) Function
A function is onto if every element in the codomain B has at least one pre-image in the domain A, meaning Range = Codomain.
Bijective Function
A function that is both one-one and onto is called bijective, which is a necessary condition for a function to be invertible.
Important Formulas
Board Exam Info
In the Madhya Pradesh (MPBSE) Class 12 Mathematics board examination, Relations and Functions typically carries around 4 to 6 marks. Expect 1 or 2 objective/multiple-choice questions (1 mark each) and one short or long-answer question (2 to 4 marks) asking you to prove whether a given relation is an equivalence relation or whether a function is bijective.
Frequently Asked Questions
How do I prove a relation is an equivalence relation?
You must prove three things step-by-step: Reflexive (show (a,a) is in R for all a), Symmetric (if (a,b) is in R, show (b,a) is in R), and Transitive (if (a,b) and (b,c) are in R, show (a,c) is in R).
Is every one-one function invertible?
No, a function must be both one-one (injective) and onto (surjective)—meaning it is bijective—to be invertible. If it is only one-one, its inverse cannot be defined for the entire codomain.
What is the easiest way to prove a function is onto?
Let y be an arbitrary element in the codomain. Express x in terms of y using the function rule f(x) = y, and verify that for every y in the codomain, the corresponding x belongs to the domain.
Learn Relations and Functions with Your AI Tutor
10 different ways to study this chapter. Free for 3 chapters per day.
Lecture
Key Points
Interactive
Quiz
Flashcards