# Class 12 Maths

## Class 12 Maths- NCERT Maths Solutions Class 12

NCERT solutions for class 12 maths chapter 1 Relations and Functions is available in pdf download. Download assignments based on Relations and functions and previous year 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.

EXPECTED BACKGROUND KNOWLEDGE

Before studying NCERT maths solutions class 12 chapter 1, 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

Relation
Suppose A and B be two sets. Then a relation R from Set B into Set A is a subset of B × A.
Types of Relations
(i) Symmetric Relation
(ii) Reflexive Relation
(iii) Transitive Relation

EQUIVALENCE RELATION
A relation R on a set A is said to be an equivalence relation on A if
(i) it is symmetric
(ii) it is reflexive
(iii) it is transitive

CLASSIFICATION OF FUNCTIONS
Suppose F be a function from A to B. assume each element of the set B is the image of at most one element of the set A i.e. whereever 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 that every 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 onto and one-to-one  is said to be a bijective function.

BINARY OPERATIONS:

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

A is said to be closed under the operation* iff for all a, b  A implies a* b  A.

The operation is said to be commutative iff a * b= b * a for all a, b A.

The operation is said to be associative iff (a * b)* c=a* (b * c) for all a, b, c   A.

An element e   A is said to be an identity element iff e * a = a = a * e

An element a   A is called invertible iff these exists some b   A such that a * b = e = b * a, b is called inverse of a.

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