Let A = { 1 , 2 , 3 , 5 } , B = { 4 , 6 , 9 } and R = { ( x , y ) : | x − y | is odd , x ∈ A and y ∈ B } . Write R in the roster form.

Given that A = { 1 , 2 , 3 , 5 } , B = { 4 , 6 , 9 } and R = { ( x , y ) : | x − y | is odd , x ∈ A and y ∈ B } . For x ∈ A and y ∈ B , we have ( x , y ) ∈ R if the modulus of difference of x and y is odd. We have to write R in the roster form. R = { ( 1 , 4 ) , ( 1 , 6 ) , ( 2 , 9 ) , ( 3 , 4 ) , ( 3 , 6 ) , ( 5 , 4 ) , ( 5 , 6 ) } Thus, R in the roster form is given by { ( 1 , 4 ) , ( 1 , 6 ) , ( 2 , 9 ) , ( 3 , 4 ) , ( 3 , 6 ) , ( 5 , 4 ) , ( 5 , 6 ) } .

Let A = { 1 , 2 , 3 , 4 , 6 } and R = { ( a , b ) : a , b ∈ A and a divides b } . Write R in the roster form.

Given that A = { 1 , 2 , 3 , 4 , 6 } and R = { ( a , b ) : a , b ∈ A and a divides b } . R is a relation on A and the ordered pair ( a , b ) ∈ R if a , b ∈ A and a divides b . ∴ 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 ) } Thus, R in the roster form is given by { ( 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 A = { 1 , 2 , 3 , 4 , 6 } and R = { ( a , b ) : a , b ∈ A and a divides b } . Find dom ( R ) and range ( R ) .

Given that A = { 1 , 2 , 3 , 4 , 6 } and R = { ( a , b ) : a , b ∈ A and a divides b } ∴ 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 ) } We have to find dom ( R ) and range ( R ) The set of all first coordinates of elements of R is called the domain of R , written as dom ( R ) The set of all second coordinates of elements of R is called the range of R , denoted by range ( R ) . ∴ dom ( R ) = { 1 , 2 , 3 , 4 , 6 } and range ( R ) = { 1 , 2 , 3 , 4 , 6 } .

Let R = { ( a , b ) ; a , b ∈ Z , and ( a − b ) is even}. Show that R is an equivalence relation on Z .

If A be a non-empty set then, a relation R on A is said to be: (i) reflexive, if ( a , a ) ∈ R for all a ∈ A , i.e., a R a for all a ∈ A (ii) symmetric, if ( a , b ) ∈ R ⇒ ( b , a ) ∈ R for all a , b ∈ A (iii) transitive, if ( a , b ) ∈ R and ( b , c ) ∈ R ⇒ ( a , c ) ∈ R for a , b , c ∈ A Given the relation R = { ( a , b ) ; a , b ∈ Z , and ( a − b ) is even} , we have to show that R is an equivalence relation. A relation is an equivalence relation if it is reflexive, symmetric and transitive. Clearly ( a , a ) ∈ R for all a ∈ Z since a - a = 0 which is an even number So, R is a reflexive relation. Now, let a , b ∈ Z such that ( a , b ) ∈ R ⇒ a - b is an even number ⇒ b - a is also even number ⇒ ( b , a ) ∈ R ⇒ R is a symmetric relation Let a , b , c ∈ Z such that ( a , b ) ∈ R and ( b , c ) ∈ R ⇒ a - b is an even number and b - c is also an even number ⇒ a - b + b - c = a - c is an even number (sum of even numbers is even) ⇒ ( a , c ) ∈ Z ⇒ R is a transitive relation Hence, R is an equivalence relation.

E M B I B E

WBCHSE Mathematics for Class 11>Set & Functions>Chapter 2 - Relations and Functions>EXERCISE 2B

R S Aggarwal Solutions for Exercise 2: EXERCISE 2B

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Exercise 2: EXERCISE 2B

Attempt the practice questions from Exercise 2: EXERCISE 2B with hints and solutions to strengthen your understanding. WBCHSE Mathematics for Class 11 solutions are prepared by Experienced Embibe Experts.

Questions from R S Aggarwal Solutions for Exercise 2: EXERCISE 2B with Hints & Solutions

EASY

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 2 - Relations and Functions>EXERCISE 2B>Q 4

Let $A = {1, 2, 3, 4, 5, 6}$ . Define a relation $R$ on $A$ by $R = {(x, y) : y = (x + 1)}$ . Write the domain, co-domain and range of $R$ .

EASY

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 2 - Relations and Functions>EXERCISE 2B>Q 5

Let $A = {1, 2, 3, 5}, B = {4, 6, 9}$ and $R = {(x, y) : | x - y | is odd, x \in A and y \in B}$ . Write $R$ in the roster form.

EASY

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 2 - Relations and Functions>EXERCISE 2B>Q 6

Let $A = {1, 2, 3, 4, 6} and R = {(a, b) : a, b \in A and a$ divides $b}$ . Write $R$ in the roster form.

EASY

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 2 - Relations and Functions>EXERCISE 2B>Q 6

Let $A = {1, 2, 3, 4, 6} and R = {(a, b) : a, b \in A and a$ divides $b}$ . Find $dom (R)$ and $range (R)$ .

EASY

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 2 - Relations and Functions>EXERCISE 2B>Q 7

Let $A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4}$ . Let $R$ be the relation, 'is greater than' from $A$ to $B$ . Write $R$ as a set of ordered pairs. Find $dom (R)$ and $range (R)$ .