Given A = 1 , 2 , 3 , 4 and B = 5 , 6 , 7 , 8 and the relation R from A to B is ' a + b = 10 , a ∈ A , b = B '. Express R as a set of ordered pairs.

Given: A = 1 , 2 , 3 , 4 and B = 5 , 6 , 7 , 8 The association between two quantities is called a Relation.A relation can be defined as 'set of ordered pairs'. The relation R from A to B is ' a + b = 10 , a ∈ A , b = B ' Put a = 2 and b = 8 ; 2 + 8 = 10 a = 3 and b = 7 ; 3 + 7 = 10 a = 4 and b = 6 ; 4 + 6 = 10 Element 1 of set A and element 5 of set B are not associated. Therefore, required set of ordered pairs is R = ( 2 , 8 ) , ( 3 , 7 ) , ( 4 , 6 )

Given A = 1 , 2 , 3 , 4 and B = 5 , 6 , 7 , 8 and the relation R from A to B is ' a + b = 10 , a ∈ A , b = B '. State the domain and range of R.

Given: A = 1 , 2 , 3 , 4 and B = 5 , 6 , 7 , 8 The relation R from A to B is ' a + b = 10 , a ∈ A , b = B ' Put a = 2 and b = 8 ; 2 + 8 = 10 a = 3 and b = 7 ; 3 + 7 = 10 a = 4 and b = 6 ; 4 + 6 = 10 Element 1 of set A and element 5 of set B are not associated. Therefore, required set of ordered pairs is R = ( 2 , 8 ) , ( 3 , 7 ) , ( 4 , 6 ) The set of all the first components of ordered pairs representing a relation is called its Domain. Domain = 2 , 3 , 4 The set of second components of the ordered pairs is called Range of the relation. Range = 8 , 7 , 6 Hence, the required answer.

Given A = 1 , 2 , 3 , 4 and B = 5 , 6 , 7 , 8 and the relation R from A to B is ' a + b = 10 , a ∈ A , b = B '. Represent R by an arrow diagram

Given: A = 1 , 2 , 3 , 4 and B = 5 , 6 , 7 , 8 The relation R from A to B is ' a + b = 10 , a ∈ A , b = B ' Put a = 2 and b = 8 ; 2 + 8 = 10 a = 3 and b = 7 ; 3 + 7 = 10 a = 4 and b = 6 ; 4 + 6 = 10 Therefore, required set of ordered pairs is R = ( 2 , 8 ) , ( 3 , 7 ) , ( 4 , 6 ) A certain relation between the elements of first set with the elements of second set is represented by Arrow diagram. Element 1 of set A and element 5 of set B are not associated. Therefore, the arrow diagram of R is :

Given the relation R = x , y | y = 6 - x , x ∈ W , y ∈ W . Express R as a set of ordered pairs.

Given the relation R = x , y | y = 6 - x , x ∈ W , y ∈ W . The association between two quantities is called a Relation.A relation can be defined as 'set of ordered pairs' The relation is y = 6 - x Put x = 0 , y = 6 - 0 ⇒ y = 6 x = 1 , y = 6 - 1 ⇒ y = 5 Similarly, for x = 2 , 3 , 4 , 5 , 6 , y = 4 , 3 , 2 , 1 , 0 Put x = 7 , y = 6 - 7 ⇒ y = - 1 which is not accepted as y ∉ W Therefore , the required set of ordered pairs is R = 0 , 6 , 1 , 5 , 2 , 4 , 3 , 3 , 4 , 2 , 5 , 1 , 6 , 0

Given the relation R = x , y | y = 6 - x , x ∈ W , y ∈ W . State the domain and range of R .

Given the relation R = x , y | y = 6 - x , x ∈ W , y ∈ W . The relation is y = 6 - x Put x = 0 , y = 6 - 0 ⇒ y = 6 x = 1 , y = 6 - 1 ⇒ y = 5 Similarly, for x = 2 , 3 , 4 , 5 , 6 , y = 4 , 3 , 2 , 1 , 0 Put x = 7 , y = 6 - 7 ⇒ y = - 1 which is not accepted as y ∉ W Therefore , the required set of ordered pairs is R = 0 , 6 , 1 , 5 , 2 , 4 , 3 , 3 , 4 , 2 , 5 , 1 , 6 , 0 The set of all the first components of ordered pairs representing a relation is called its Domain. Domain = 0 , 1 , 2 , 3 , 4 , 5 , 6 The set of second components of the ordered pairs is called Range of the relation. Range = 6 , 5 , 4 , 3 , 2 , 1 , 0 Hence, the required answer.

Given the relation R = x , y | y = 6 - x , x ∈ W , y ∈ W . Represent R by an arrow diagram

Given the relation R = x , y | y = 6 - x , x ∈ W , y ∈ W The relation is y = 6 - x Put x = 0 , y = 6 - 0 ⇒ y = 6 x = 1 , y = 6 - 1 ⇒ y = 5 Similarly, for x = 2 , 3 , 4 , 5 , 6 , y = 4 , 3 , 2 , 1 , 0 Put x = 7 , y = 6 - 7 ⇒ y = - 1 which is not accepted as y ∈ W Therefore , the required set of ordered pairs is R = 0 , 6 , 1 , 5 , 2 , 4 , 3 , 3 , 4 , 2 , 5 , 1 , 6 , 0 A certain relation between the elements of first set with the elements of second set is represented by Arrow diagram. From the relation set it is observed that all the elements of first set are associated with the elements of second set. Therefore, the arrow diagram of R is :

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ICSE Skills In Mathematics>Algebra>Chapter 22 - Relations and Functions>EXERCISE 22(A)

V K Raman and S N Sharma Solutions for Exercise 1: EXERCISE 22(A)

Author:V K Raman & S N Sharma

V K Raman Mathematics Solutions for Exercise - V K Raman and S N Sharma Solutions for Exercise 1: EXERCISE 22(A)

Attempt the practice questions from Exercise 1: EXERCISE 22(A) with hints and solutions to strengthen your understanding. ICSE Skills In Mathematics solutions are prepared by Experienced Embibe Experts.