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NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions provides solutions for all the questions enlisted under the chapter, which is included in the CBSE syllabus 2023-24. All exercise questions are solved using a step-by-step approach. Solving the questions from the Class 12 Maths NCERT textbook helps grasp the concepts correctly ...
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To download our free pdf of Chapter 1 – Relations and Functions Maths NCERT Solutions for Class 12 to help you to score more marks in your board exams and as well as competitive exams. Download the FREE PDF. About MathonGo. MathonGo is the one stop destination for all your Math requirements. NCERT Book Solutions.
www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more) Mathematics Notes for Class 12 chapter 1. Relations and Functions Relation If A and B are two non-empty sets, then a relation R from A to B is a subset of A x B.
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- Answer: Let A={1,2,3} A relation R on A is defined as R={(1,2),(2,1)}. It is seen that (1,1),(2,2),(3,3)∈/R. ∴R is not reflexive. Now, as (1,2)∈R a...
- Answer: Let A={4,6,8} Define a relation R on A as: A={(4,4),(6,6),(8,8),(4,6),(6,4),(6,8),(8,6)} Relation R is reflexive since for every {a∈A,(a,a)...
- Answer: R={(x,y):x is the father of y} (x,x)∈/R As x cannot be the father of himself. ∴R is not reflexive. Now, let (x,y)∈R ⇒x is the father of y....
- Answer: It is given that A={1,2,3}, B={4,5,6,7}. f:A→B is defined as f=(1,4),(2,5),(3,6). ∴f(1)=4,f(2)=5,f(3)=6 It is seen that the images of disti...
- Relation
- Types of Relations
- Functions
- Types of Function
- Binary Operations
It defines the relationship between two sets of values, let say from set A to set B.Set A is then called domain and set B is then called codomain.Empty Relation:In this there is no relation between any element of a set.It is also known as void relationFor example: if set A is $\left\{ 2,4,6 \right\}$ then an empty relation can be $R=\left\{ x,y \right\}$where $x+y>11$Universal Relation:In this each element of a set is related to every element of that set.A function f from a set A to a set B is a rule which associates each element of set A to a unique element of set B.
One-One Function:A function f from set A to set B is called one-one function if no two distinct elements of A have the same image in B.Mathematically, a function f from set A to set B if $f\left( x \right)=f\left( y \right)$ implies that $x=y$ for all $x,y\in A$.One-one function is also called an injectivefunction.Onto Function:A function f from set A to set B is called onto function if each element of set B has a preimage in set A or range of function f is equal to the codomain i.e., set B.A binary operation are mathematical operations such as addition, subtraction, multiplication and division performed between two operands.A binary operation on a set A is defined as operations performed between two elements of set A and the result also belongs to set A. Then set A is called binary composition.It is denoted by $*$For example: Binary addition of real numbers is a binary composition since by adding two real numbers the result will always be a real number.Transitive relation R in X is a relation satisfying (a, b) ∈ R and (b, c) ∈ R implies that (a, c) ∈ R. Equivalence relation R in X is a relation which is reflexive, symmetric and transitive. Functions Functions are defined as a special kind of relations. Types of Functions 1) One-one Function A function f : X → Y is one-one (or ...
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Class 12 Mathematics | NCERT Solutions | Relations and Functions www.learnohub.com Exercise 1.1 Question 1: Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A = {1, 2, 3...13, 14} defined as R = {(x, y): 3x − y = 0} (ii) Relation R in the set N of natural numbers defined as
