Let A × B = { ( a , b ) : b = 3 a - 2 } . if ( x , - 5 ) and ( 2 , y ) belong to A × B , find the values of x and y .

Given: A × B = { ( a , b ) : b = 3 a - 2 } and { ( x , - 5 ) , ( 2 , y ) } ∈ A × B For ( x , - 5 ) ∈ A × B b = 3 a - 2 ⇒ - 5 = 3 ( x ) - 2 ⇒ - 5 + 2 = 3 x ⇒ - 3 = 3 x ⇒ x = - 1 For ( 2 , y ) ∈ A × B b = 3 a - 2 ⇒ y = 3 ( 2 ) - 2 ⇒ y = 6 - 2 ⇒ y = 4 Hence, the value of x = - 1 and y = 4

Let A and B be two sets such that n ( A ) = 3 and n ( B ) = 2 . If a ≠ b ≠ c and ( a , 0 ) , ( b , 1 ) , ( c , 0 ) is in A × B , find A and B .

Since, ( a , 0 ) , ( b , 1 ) , ( c , 0 ) are the elements of A × B . It is given that n ( A ) = 3 and n ( B ) = 2 Then, a , b , c ∈ A and 0 , 1 ∈ B ∴ a , b , c ∈ A and n ( A ) = 3 ⇒ A = { a , b , c ] and 0 , 1 ∈ B and n ( B ) = 2 ⇒ B = { 0 , 1 }

If A = { - 2 , 2 } and B = 0 , 3 , 5 , then find A × B .

Given: A = { - 2 , 2 } and B = { 0 , 3 , 5 } To find: A × B By the definition of the Cartesian product, Given two non - empty sets P and Q . The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q , i.e. P × Q = { ( p , q ) : p ∈ P , q ∈ Q } Here, A = { - 2 , 2 } and B = { 0 , 3 , 5 } . So, A × B = { ( - 2 , 0 ) , ( - 2 , 3 ) , ( - 2 , 5 ) , ( 2 , 0 ) , ( 2 , 3 ) , ( 2 , 5 ) }

Let A = { - 2 , 2 } and B = ( 0 , 3 , 5 ) . Find B × A .

Given: A = { - 2 , 2 } and B = { 0 , 3 , 5 } To find : B × A By the definition of the Cartesian product, Given two non - empty sets P and Q . The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q i.e. P × Q = { ( p , q ) : p ∈ P , q ∈ Q } Here, A = { - 2 , 2 } and B = { 0 , 3 , 5 } . So, B × A = { ( 0 , - 2 ) , ( 0 , 2 ) , ( 3 , - 2 ) , ( 3 , 2 ) , ( 5 , - 2 ) , ( 5 , 2 ) }

Let A = { - 2 , 2 } and B = ( 0 , 3 , 5 ) . Find A × A .

Given: A = { - 2 , 2 } By the definition of the Cartesian product Given two non - empty sets P and Q . The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q i.e. P × Q = { ( p , q ) : p ∈ P , q ∈ Q } Here, A = { - 2 , 2 } and A = { - 2 , 2 } . So, A × A = { ( - 2 , - 2 ) , ( - 2 , 2 ) , ( 2 , - 2 ) , ( 2 , 2 ) }

Let A = { - 2 , 2 } and B = ( 0 , 3 , 5 ) . Find B × B .

Given: B = { 0 , 3 , 5 } To find : B × B By the definition of the Cartesian product, Given two non - empty sets P and Q . The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q , i.e. P × Q = { ( p , q ) : p ∈ P , q ∈ Q } Here, B = { 0 , 3 , 5 } and B = { 0 , 3 , 5 } . So, B × B = { ( 0 , 0 ) , ( 0 , 3 ) , ( 0 , 5 ) , ( 3 , 0 ) , ( 3 , 3 ) , ( 3 , 5 ) , ( 5 , 0 ) , ( 5 , 3 ) , ( 5 , 5 ) }

If A = 5 , 7 , find A × A .

We have, A = { 5 , 7 } So, By the definition of the Cartesian product. Given two non - empty sets P and Q . The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q i.e. P × Q = { ( p , q ) : p ∈ P , q ∈ Q } Here, A = 5 , 7 . So, A × A = { ( 5 , 5 ) , ( 5 , 7 ) , ( 7 , 5 ) , ( 7 , 7 ) }

If A = 5 , 7 , find A × A × A .

We have, A = { 5 , 7 } So, By the definition of the Cartesian product. Given two non - empty sets P and Q . The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q i.e. P × Q = { ( p , q ) : p ∈ P , q ∈ Q } Here, A = 5 , 7 . So, A × A = { ( 5 , 5 ) , ( 5 , 7 ) , ( 7 , 5 ) , ( 7 , 7 ) } Now again, we apply the definition of Cartesian product to find A × A × A Here, A = { 5 , 7 } and A × A = { ( 5 , 5 ) , ( 5 , 7 ) , ( 7 , 5 ) , ( 7 , 7 ) } ∴ A × A × A = { ( 5 , 5 , 5 ) , ( 5 , 5 , 7 ) , ( 5 , 7 , 5 ) , ( 5 , 7 , 7 ) , ( 7 , 5 , 5 ) , ( 7 , 5 , 7 ) , ( 7 , 7 , 5 ) , ( 7 , 7 , 7 ) }

E M B I B E

Senior Secondary School Mathematics FOR CLASS 11>Set and Functions>Chapter 2 - Relations>EXERCISE 2A

R S Aggarwal Solutions for Exercise 1: EXERCISE 2A

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Exercise 1: EXERCISE 2A

Attempt the practice questions from Exercise 1: EXERCISE 2A with hints and solutions to strengthen your understanding. Senior Secondary School Mathematics FOR CLASS 11 solutions are prepared by Experienced Embibe Experts.

Questions from R S Aggarwal Solutions for Exercise 1: EXERCISE 2A with Hints & Solutions

MEDIUM

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 2 - Relations>EXERCISE 2A>Q 10

Let $A \times B = {(a, b) : b = 3 a - 2} . if (x, - 5) and (2, y)$ belong to $A \times B,$ find the values of $x$ and $y$ .

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 2 - Relations>EXERCISE 2A>Q 11

Let $A$ and $B$ be two sets such that $n (A) = 3$ and $n (B) = 2 .$ If $a \neq b \neq c$ and $(a, 0), (b, 1), (c, 0)$ is in $A \times B,$ find $A$ and $B$ .