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>Chapter 2 - Relations and Functions>EXERCISE 2.2

Tripura Board Solutions for Chapter: Relations and Functions, Exercise 2: EXERCISE 2.2

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Tripura Board Mathematics Solutions for Exercise - Tripura Board Solutions for Chapter: Relations and Functions, Exercise 2: EXERCISE 2.2

Attempt the free practice questions on Chapter 2: Relations and Functions, Exercise 2: EXERCISE 2.2 with hints and solutions to strengthen your understanding. Mathematics solutions are prepared by Experienced Embibe Experts.

Questions from Tripura Board Solutions for Chapter: Relations and Functions, Exercise 2: EXERCISE 2.2 with Hints & Solutions

EASY

11th Tripura Board

IMPORTANT

Mathematics>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

11th Tripura Board

IMPORTANT

Mathematics>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

11th Tripura Board

IMPORTANT

Mathematics>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

11th Tripura Board

IMPORTANT

Mathematics>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 $R$ .