NCERT solutions for class 12 maths chapter 1 exercise 1.1, 1.2, 1.3, 1.4 and miscellaneous of Relations and Functions free pdf download. Download assignments based on Relations and functions and Previous Years Questions asked in CBSE board, important questions for practice as per latest CBSE Syllabus for 2017 – 2018. Revision book is provided for the complete revision of this chapter including solved example and exercises. Download books in pdf form or buy NCERT books online.
NCERT solutions for class 12 maths chapter 1 Relations and Functions
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Assignments for practice
Mixed Chapter Tests
Chapter 1, 2, 3 & 4
Level 1 Test 1
Level 2 Test 1
EXPECTED BACKGROUND KNOWLEDGE
Before studying this lesson, you should know:
- Concept of set, types of sets, operations on sets
- Concept of ordered pair and cartesian product of set.
- Domain, co-domain and range of a relation and a function
Let A and B be two sets. Then a relation R from Set A into Set B is a subset of A × B.
Types of Relations
(i) Reflexive Relation
(ii) Symmetric Relation
(iii) Transitive Relation
A relation R on a set A is said to be an equivalence relation on A iff
(i) it is reflexive
(ii) it is symmetric
(iii) it is transitive
CLASSIFICATION OF FUNCTIONS
Let f be a function from A to B. If every element of the set B is the image of at least one element of the set A i.e. if there is no unpaired element in the set B then we say that the function f maps the set A onto the set B. Otherwise we say that the function maps the set A into the set B.
Functions for which each element of the set A is mapped to a different element of the set B are said to be one-to-one.
A function can map more than one element of the set A to the same element of the set B. Such a type of function is said to be many-to-one. A function which is both one-to-one and onto is said to be a bijective function.
Let A, B be two non-empty sets, then a function from A × A to A is called a binary operation on A.
If a binary operation on A is denoted by *, the unique element of A associated with the ordered pair (a, b) of A × A is denoted by a * b.
The order of the elements is taken into consideration, i.e. the elements associated with the pairs (a, b) and (b, a) may be different i.e. a * b may not be equal to b * a.
Let A be a non-empty set and ‘*’ be an operation on A, then