Let A = 1 , 2 , 3, 4 , 6 . Let R be the relation on A defined by { ( a , b ) : a , b ∈ A , b is exactly divisible by a } . Write R in roster form

Given, A = { 1 , 2 , 3 , 4 , 6 } We know that a relation R on set A is a subset of the cartesian product A × A . Here, the relation R on set A is defined as: R = { ( a , b ) : a , b ∈ A , b is exactly divisible by a } Since a , b ∈ A Let, a = 1 , b = 2 then b a = 2 1 = 2 , here b is exactly divisible by a . So 1 , 2 ∈ R if a = 1 , b = 3 then b a = 3 1 = 3 , here b is exactly divisible by a . So, 1 , 3 ∈ R . Similarly we can check for a = 1 , b = 1 , 4 , 6 Now, if a = 2 and b = 3 then b a = 3 2 , here b is not exactly divisible by a . So, 2 , 3 ∉ R if a = 2 and b = 1 then b a = 1 2 , here b is not exactly divisible by a . So, 2 , 1 ∉ R Similarly, we can check for other elements of R Thus the roster form of R is, R = { ( 1 , 1 ) , ( 1 , 2 ) , ( 1 , 3 ) , ( 1 , 4 ) , ( 1 , 6 ) , ( 2 , 2 ) , ( 2 , 4 ) , ( 2 , 6 ) , ( 3 , 3 ) , ( 3 , 6 ) , ( 4 , 4 ) , ( 6 , 6 ) }

Let R be the relation on Z defined by R = a , b : a , b ∈ Z , a - b i s a n i n t e g e r . Find the domain and range of R .

The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Given relation is, R = { ( a , b ) : a , b ∈ Z , a - b i s a n i n t e g e r } We know that the difference between any two integers is always an integer. Therefore, Domain of R = Z And, Range of R = Z

E M B I B E

MATHEMATICS Textbook for Class XI>Chapter 2 - Relations and Functions>EXERCISE 2.2

EXERCISE 2.2

Author:Jharkhand Board

Jharkhand Board Mathematics Solutions for EXERCISE 2.2

Simple step-by-step solutions to EXERCISE 2.2 questions of Relations and Functions from MATHEMATICS Textbook for Class XI. Also get 3D topic explainers, cheat sheets, and unlimited doubts solving on EMBIBE.

Questions from EXERCISE 2.2 with Hints & Solutions

EASY

1th Jharkhand Board

IMPORTANT

MATHEMATICS Textbook for Class XI>Chapter 2 - Relations and Functions>EXERCISE 2.2>Q 4

The figure shows a relationship between the sets $P$ and $Q .$ Write this relation in Roster form.
What is it’s domain and range?
Question Image

MEDIUM

1th Jharkhand Board

IMPORTANT

MATHEMATICS Textbook for Class XI>Chapter 2 - Relations and Functions>EXERCISE 2.2>Q 5

Let $A = \{1, 2, 3, 4, 6\} .$ Let $R$ be the relation on $A$ defined by ${(a, b) : a, b \in A, b$ is exactly divisible by $a}$ .
Write $R$ in roster form

MEDIUM

1th Jharkhand Board

IMPORTANT

MATHEMATICS Textbook for Class XI>Chapter 2 - Relations and Functions>EXERCISE 2.2>Q 5

Let $A = \{1, 2, 3, 4, 6\} .$ Let $R$ be the relation on $A$ defined by ${(a, b) : a, b \in A, b$ is exactly divisible by $a}$ . Find the number of elements in the domain of $R$ .

EASY

1th Jharkhand Board

IMPORTANT

MATHEMATICS Textbook for Class XI>Chapter 2 - Relations and Functions>EXERCISE 2.2>Q 5

Let $A = \{1, 2, 3, 4, 6\}$ . Let $R$ be the relation on $A$ defined by ${(a, b) : a, b \in A, b$ is exactly divisible by $a}$ . Find the number of elements in the set of range of $R$ .