Class 12 Maths - CBSE
Relations and Functions
The Chapter Relations and Functions in Class 12 Mathematics builds upon the basic concepts of sets learned in Class 11. It explores advanced types of relations such as reflexive, symmetric, transitive, and equivalence relations. Furthermore, it delves into functions, focusing heavily on injective (one-one), surjective (onto), and bijective functions, alongside the concept of invertible functions and binary operations. This chapter is foundational for calculus and algebra. In CBSE board exams, it carries significant weight, usually around 6 to 8 marks, testing students' logical reasoning and proof-writing skills through standard theorem-based and numerical problems.
Start Learning FreeKey Concepts
Reflexive Relation
A relation R on a set A is reflexive if every element relates to itself, meaning (a, a) belongs to R for all a in A.
Equivalence Relation
A relation is 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 in A have distinct images in B, meaning f(x1) = f(x2) implies x1 = x2.
Onto (Surjective) Function
A function f from A to B is onto if every element in the codomain B has at least one pre-image in the domain A.
Invertible Function
A function is invertible if and only if it is both one-one and onto (bijective), allowing the definition of a unique inverse function.
Important Formulas
Board Exam Info
In the CBSE Class 12 Mathematics board exam, Relations and Functions typically carries around 6 to 8 marks. Questions usually appear as one 1-mark MCQ, one 2-mark short answer, and one 4-mark or 5-mark long answer question. Common question types include checking whether a given relation is an equivalence relation, proving a function is one-one and onto, and finding the inverse of a given bijective function.
Frequently Asked Questions
How do I prove a relation is an equivalence relation?
You must separately prove three properties: Reflexive ((a,a) in R), Symmetric (if (a,b) in R then (b,a) in R), and Transitive (if (a,b) and (b,c) in R then (a,c) in R) for all elements in the set using general variables, not just numbers.
What is the easiest way to prove a function is one-one?
Assume f(x1) = f(x2) for any two elements x1 and x2 in the domain, and algebraically simplify the equation until you successfully prove that x1 = x2.
Do I need to check both domain and codomain for onto functions?
Yes. To prove onto, you must show that for every arbitrary element y in the codomain, there exists an element x in the domain such that f(x) = y.
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