If a ∈ { - 1 , 2 , 3 , 4 , 5 } and b ∈ 0 , 3 , 6 write the set of all ordered pairs ( a , b ) such that a + b = 5

Given: a ∈ - 1 , 2 , 3 , 4 , 5 and b ∈ 0 , 3 , 6 such that a + b = 5 We know: - 1 + 6 = 5 , 2 + 3 = 5 , and 5 + 0 = 5 Thus, possible ordered pairs a , b are { ( - 1 , 6 ) , ( 2 , 3 ) , ( 5 , 0 ) } .

If A = { 1 , 2 } and B = { 1 , 3 } , find A × B and B × A .

Given: A = { 1 , 2 } and B = { 1 , 3 } A × B = { 1 , 2 } × { 1 , 3 } = { ( 1 , 1 ) , ( 1 , 3 ) , ( 2 , 1 ) , ( 2 , 3 ) } B × A = { 1 , 3 } × { 1 , 2 } = { ( 1 , 1 ) , ( 1 , 2 ) , ( 3 , 1 ) , ( 3 , 2 ) }

Let A = { 1 , 2 , 3 } and B = { 3 , 4 } . Find A × B and show it graphically.

Given: A = { 1 , 2 , 3 } and B = { 3 , 4 } A × B = { 1 , 2 , 3 } × { 3 , 4 } = { ( 1 , 3 ) , ( 1 , 4 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 3 ) , ( 3 , 4 ) } Steps to follow to represent A × B graphically, Step 1 : One horizontal and one vertical axis should be drawn Step 2 : Elements of set A should be represented in horizontal axis and on vertical axis elements of set B should be represented Step 3 : Draw dotted lines perpendicular to horizontal and vertical axes through the elements of set A and B Step 4 : Point of intersection of these perpendicular represents A × B

If A = 1 , 2 , 3 and B = 2 , 4 , what are A × B , B × A , A × A , B × B , and ( A × B ) ∩ ( B × A ) ?

Given: A = { 1 , 2 , 3 } and B = { 2 , 4 } Now let us find A × B , B × A , A × A , ( A × B ) ∩ ( B × A ) A × B = { 1 , 2 , 3 } × { 2 , 4 } = { ( 1 , 2 ) , ( 1 , 4 ) , ( 2 , 2 ) , ( 2 , 4 ) , ( 3 , 2 ) , ( 3 , 4 ) } B × A = { 2 , 4 } × { 1 , 2 , 3 } = { ( 2 , 1 ) , ( 2 , 2 ) , ( 2 , 3 ) , ( 4 , 1 ) , ( 4 , 2 ) , ( 4 , 3 ) } A × A = { 1 , 2 , 3 } × { 1 , 2 , 3 } = { ( 1 , 1 ) , ( 1 , 2 ) , ( 1 , 3 ) , ( 2 , 1 ) , ( 2 , 2 ) , ( 2 , 3 ) , ( 3 , 1 ) , ( 3 , 2 ) , ( 3 , 3 ) } B × B = { 2 , 4 } × { 2 , 4 } = { ( 2 , 2 ) , ( 2 , 4 ) , ( 4 , 2 ) , ( 4 , 4 ) } Intersection of two sets represents common elements of both the sets. So, ( A × B ) ∩ ( B × A ) = { ( 2 , 2 ) }

Let A and B be two sets such that n ( A ) = 3 and n ( B ) = 2 . If ( x , 1 ) , ( y , 2 ) , ( z , 1 ) are in A × B , find A and B , where x , y , z are distinct elements.

A is the set of all first entries in ordered pairs in A × B and B is the set of all second entries in ordered pairs in A × B Also, n ( A ) = 3 and n ( B ) = 2 A × B = ( x , 1 ) , ( y , 2 ) , ( z , 1 ) ∴ A = { x , y , z } and B = { 1 , 2 }

Let A = { 1 , 2 , 3 , 4 } and R = { ( a , b ) : a ∈ A , b ∈ A , a divides b } . Write R explicitly.

A = { 1 , 2 , 3 , 4 } R = { ( a , b ) : a ∈ A , b ∈ A , a divides b } We know, 1 divides 1 , 2 , 3 and 4 , 2 divides 2 and 4 , 3 divides 3 , 4 divides 4 . ∴ R = { ( 1 , 1 ) , ( 1 , 2 ) , ( 1 , 3 ) , ( 1 , 4 ) , ( 2 , 2 ) , ( 2 , 4 ) , ( 3 , 3 ) , ( 4 , 4 ) }

E M B I B E

MATHEMATICS for CLASS XI>Chapter 2 - Relations>EXERCISE 2.1

R D Sharma Solutions for Chapter: Relations, Exercise 1: EXERCISE 2.1

Author:R D Sharma

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Relations, Exercise 1: EXERCISE 2.1

Attempt the practice questions on Chapter 2: Relations, Exercise 1: EXERCISE 2.1 with hints and solutions to strengthen your understanding. MATHEMATICS for CLASS XI solutions are prepared by Experienced Embibe Experts.

Questions from R D Sharma Solutions for Chapter: Relations, Exercise 1: EXERCISE 2.1 with Hints & Solutions

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 2 - Relations>EXERCISE 2.1>Q 3

If $a \in {- 1, 2, 3, 4, 5}$ and $b \in \{0, 3, 6\}$ write the set of all ordered pairs $(a, b)$ such that $a + b = 5$

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 2 - Relations>EXERCISE 2.1>Q 4

If $a \in {2, 4, 6, 9}$ and $b \in {4, 6, 18, 27}$ , then form the set of all ordered pairs $(a, b)$ such that $a$ divides $b$ and $a < b$ .

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 2 - Relations>EXERCISE 2.1>Q 5

If $A = {1, 2}$ and $B = {1, 3}$ , find $A \times B$ and $B \times A$ .

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 2 - Relations>EXERCISE 2.1>Q 6

Let $A = {1, 2, 3}$ and $B = {3, 4}$ . Find $A \times B$ and show it graphically.

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 2 - Relations>EXERCISE 2.1>Q 7

If $A = \{1, 2, 3\}$ and $B = \{2, 4\}$ , what are $A \times B, B \times A, A \times A, B \times B$ , and $(A \times B) \cap (B \times A)$ ?

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 2 - Relations>EXERCISE 2.1>Q 8

If $A$ and $B$ are two sets having $3$ elements in common. If $n (A) = 5, n (B) = 4$ , find $n (A \times B)$ and $n [(A \times B) \cap (B \times A)]$ .

EASY

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 2 - Relations>EXERCISE 2.1>Q 10

Let $A$ and $B$ be two sets such that $n (A) = 3$ and $n (B) = 2$ . If $(x, 1), (y, 2), (z, 1)$ are in $A \times B$ , find $A$ and $B$ , where $x, y, z$ are distinct elements.