CBSE Mathematics

Class 12  chapter 1 Relations and functions Basic concepts of topic relations and functions class XII chapter 1 of mathematics. Equivalence relations, different types of functions, composition and inverse of functions. Introduction In class 11 we have studied about Cartesian product of two sets, relations, functions, domain, range and co-domains. Now in this chapter we have studied about the different types of relations, different types of functions, composition of functions and invertible functions. Relations A relation R from set A to set B is the subset of Cartesian product A x B. In Cartesian product A x B number of relations equal to the number of subsets. Domain Set of all first elements of the ordered pairs in the relation R is called its domain. Range Set of all second elements of the ordered pairs in the relation R is called its range. In any ordered pair second element is also called the image of first element. Types of relation

Relation & Functions Basic concepts on relations and functions chapter 2 of class 11, basic point based on the topic relation and functions. Different types of functions and their graphs. Introduction In our daily life we come across different types of relations like brother and sister, father and son, husband and wife etc.  Topics to be discussed Here Ordered Pair Cartesian Product of two sets Relations complete explanations. Domain, Range and Co-domain of relations. Functions and Different types of functions. Graphs of the Functions. Undefined Terms. Cartesian Product of two sets If A and B are two sets then Cartesian product A X B is the set of all ordered pairs of elements from A to B, i.e.           A X B = { (a, b) : a ∈ A, b ∈ B } First element of all the ordered pair  belongs to set A and second element belongs to set B. If either A or B is a null set, then A X B will also be  empty set. In this case we can write A X B = φ

Set Theory, Chapter1, Class-11 Basic concepts and formulas based on set theory chapter 1 cbse class 11. Useful and important points based on set theory. Revision notes of chapter 1 class 11 set theory. Introduction Of Set Theory The concept of sets serves as a fundamental part of the present day mathematics. Sets are used to define the concepts of relations and functions. The study of geometry sequences, probability etc. requires the knowledge of sets. The theory of sets developed by German Mathematician Georg Cantor(1845 - 1918) Few examples of sets are given below N : the set of all natural numbers. W : the set of all whole numbers. Z : the set of all integers. Q : the set of all rational numbers. R : the set of all real numbers. Z + : The set of positive integers. Q + : The set of positive rational numbers. R + : The set of positive real numbers. Definition of set A  collection of  well defined and different  object