A relation R is defined from a set A = 2 , 6 , 8 , 10 to a set B = 2 , 3 , 4 , 5 by R = a , b : a ∈ A , b ∈ B , a is divisible by b . Find R as a set of ordered pairs. Find also the domain and range of R .

Given A = 2 , 6 , 8 , 10 and B = 2 , 3 , 4 , 5 R be a relation from A into B defined by R = a , b : a ∈ A , b ∈ B , a is divisible by b Then R = ( 2 , 2 ) , ( 6 , 2 ) , ( 6 , 3 ) , ( 8 , 2 ) , ( 8 , 4 ) , ( 10 , 2 ) , ( 10 , 5 ) . So, Domain of R = 2 , 6 , 8 , 10 and Range of R = 2 , 3 , 4 , 5

Find the domain and range of the following relation. { ( x , y ) : x ∈ N , y ∈ N and x + y = 8 }

A relation is a set of ordered pairs. If A and B be any two non-empty sets, then a relation R from the set A to the set B is a subset of A × B . In this case, an element a of A is said to be related to an element b of B by R and we express this by the symbol a R b , where ( a , b ) ∈ R . If R is a relation from A to B , then the domain of R is the set of all first components of the ordered pairs in R and the range of R is the set of all second components of all ordered pairs in R . Thus, the domain of R = { a : ( a , b ) ∈ R } and range of R = { b : ( a , b ) ∈ R } . The given relation is { ( x , y ) : x ∈ N , y ∈ N and x + y = 8 } . We get, 1 + 7 = 8 , 2 + 6 = 8 , 3 + 5 = 8 , 4 + 4 = 8 , 5 + 3 = 8 , 6 + 2 = 8 and 7 + 1 = 8 . Hence, the relation R can be written as 1 , 7 , 2 , 6 , 3 , 5 , 4 , 4 , 5 , 3 , 6 , 2 , 7 , 1 . Therefore, the domain is 1 , 2 , 3 , 4 , 5 , 6 , 7 and the range is 1 , 2 , 3 , 4 , 5 , 6 , 7 .

E M B I B E

I.S.C MATHEMATICS FOR CLASS XI>Chapter 2 - Relations and Functions>EXERCISE-2(II)>Q 9

EASY

11th ICSE

IMPORTANT

Earn 100

Let $R$ be the relation on the set $N$ of natural numbers defined by $a + 3 b = 12 .$ Find $R .$

Important Questions on Relations and Functions

EASY

11th ICSE

IMPORTANT

I.S.C MATHEMATICS FOR CLASS XI>Chapter 2 - Relations and Functions>EXERCISE-2(II)>Q 9

Let $R$ be the relation on the set $N$ of natural numbers defined by $a + 3 b = 12 .$ Find the range of $R .$

EASY

11th ICSE

IMPORTANT

I.S.C MATHEMATICS FOR CLASS XI>Chapter 2 - Relations and Functions>EXERCISE-2(II)>Q 9

Let $R$ be the relation on the set $N$ of natural numbers defined by $a + 3 b = 12 .$ Find the domain of $R .$

EASY

11th ICSE

IMPORTANT

I.S.C MATHEMATICS FOR CLASS XI>Chapter 2 - Relations and Functions>EXERCISE-2(II)>Q 10

A relation $R$ is defined from a set $A = \{2, 6, 8, 10\}$ to a set $B = \{2, 3, 4, 5\}$ by $R = \{(a, b) : a \in A, b \in B, a is divisible by b\}$ . Find $R$ as a set of ordered pairs. Find also the domain and range of $R$ .