Relations and Functions

# Relations and Functions

Edited By Team Careers360 | Updated on May 07, 2022 11:49 AM IST

Introduction:
In relations and functions Class 11, you will learn the cartesian product of sets along with relations and functions. In our day-to-day life, we have known the term relations in a pattern such as the relation between brothers and sisters, husband and wife, or teacher and student. In Maths, the term relation is used to relate the numbers, symbols, variables, sets, group of sets, etc. For example, A is a subset of B denotes the relation of A and B. A function is a kind of relation which is operated between two quantities to yield output.

Class 12 Chapter 1 starts with the revision of the general notation of relations and functions. Students have already learned about the domain, co-domain, and range in class 11 along with the various types of specific real-valued functions and the respective graphs. In class 12 Maths Chapter 1, students will learn about different types of relations and functions, the composition of functions, etc., in detail.

### List of topics according to NCERT and JEE Main/NEET syllabus

1. Cartesian Products of Sets
2. Relations
3. Functions
4. Inverse Relation
5. Types of Relation
6. Reflexive
7. Symmetric
8. Transitive
9. Equivalence
1. Types of Functions
1. One-one
2. Onto
3. Bijective (both one-one and onto)
1. Composition of Functions and Invertible Function
2. Binary Operations

### Important concepts and Laws

• Relations
• Equivalence Relation
• Functions
• Binary operations

### Importance of Sets class 11/12

We come across many relations in our daily lives, such as number x is more significant than number y, triangle m is similar to triangle n, and set A is a subset of set B. See, there is some relationship between the pairs of objects in a specific order in all of these. Thus, Relations and functions are crucial for arithmetic. Practising Class 11 Maths NCERT Chapter 2 will ensure a thorough understanding of essential topics centred on Relations and Functions.

Although, in the JEE test, there are two or three questions from Relation and Functions.

However, it is still very important.

Relation and Function are quite important from the exam point of view. In mathematics, “sets, relations, and functions” is one of the most important topics of set theory. Sets, relations, and functions are three different words having different meanings mathematically but equally important for the preparation of JEE mains.

NCERT Exemplar Solutions Subject wise link:

1. What is the difference between functions and relations in mathematics, and is every relation a function?

Sometimes it's not easy to identify the differences between functions and relations in mathematics. An ordered pair is a set of inputs and outputs that represent a relationship between any two values. A relation is defined as a set of inputs and outputs, while a function is defined as a relation with one output for each input.

A function contains a unique value to each finite sequence of objects known as the arguments.

In reality, every function is fundamentally a relation. However, not every relationship may be classified as a function.

2. What is an example of an inverse relation?

A pair of functions that are inverse to each other is a third example of an inverse relationship in mathematics. Assume you enter the numbers 2, 3, 4, and 5 into the function. y = 2 x + 1 y = 2x + 1 y = 2x + 1 y=2x+1 You will receive the following points: (2,5), (3,7), (4,9), and (5,10) (5,11)

3. Do all functions have an inverse?

A function has an inverse if and only if it is a one-to-one function. That is, for every element of the range there is exactly one corresponding element in the domain. To use an example f(x), f(x) is one-to-one if and only if for every value of f(x) there is exactly one value of x that gives that value.

4. How do you determine a relation of the set?

A relation from a set A to a set B is a subset of AB. As a result, a relation R is made up of ordered pairs (a,b), where aA and bB.

5. Is a function a set of ordered pairs?

A function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate.

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