List all the elements of the set: E = x : x ∈ Z and x 2 = x .

Given: x ∈ Z and x 2 = x Z is a set of integers Integers are … - 2 , - 1 , 0 , 1 , 2 , … Now, if we take x = - 2 , then we have to check that it satisfies the given condition x 2 = x ( - 2 ) 2 = 4 ≠ 2 So, - 2 ∉ E If x = - 1 then ( - 1 ) 2 = 1 ≠ - 1 [not satisfying x 2 = x ] So, - 2 ∉ E If x = 0 then ( 0 ) 2 = 0 [ satisfying x 2 = x ∴ 0 ∈ E If x = 0 then ( 1 ) 2 = 1 [ Satisfying x 2 = x ∴ 1 ∈ E If x = 2 then ( 2 ) 2 = 4 ≠ 2 [ Not satisfying x 2 = x ⇒ 2 ∉ E Therefore, all elements of the set E = { 0 , 1 } .

List all the elements of the set: F = x : x = ∈ Z and - 1 2 < X 13 2

Given x ∈ Z and - 1 2 < x < 13 2 We have to find all elements of the set F It can be seen that - 1 2 = - 0 . 5 ; 13 2 = 6 . 5 We know that, Z denotes set of integers Hence, all elements of the set F = { 0 , 1 , 2 , 3 , 4 , 5 , 6 } .

List all the elements of the set given below. G = x : x = 1 ( 2 n - 1 ) ' n ∈ N and 1 ≤ n ≤ 5

Given: x = 1 2 n - 1 and 1 ≤ n ≤ 5 So, n = 1 , 2 , 3 , 4 , 5 If n = 1 , then x = 1 2 n - 1 = 1 2 ( 1 ) - 1 = 1 1 = 1 If n = 2 , then x = 1 2 n - 1 = 1 2 ( 2 ) - 1 = 1 4 - 1 = 1 3 If n = 3 , then x = 1 2 n - 1 = 1 2 ( 3 ) - 1 = 1 6 - 1 = 1 5 If n = 4 , then x = 1 2 n - 1 = 1 2 ( 4 ) - 1 = 1 8 - 1 = 1 7 If n = 5 , then x = 1 2 n - 1 = 1 2 ( 5 ) - 1 = 1 10 - 1 = 1 9 So, G = 1 , 1 3 , 1 5 , 1 7 , 1 9

List all the elements of the set given below. H = { x : x ∈ Z , | x | ≤ 2 }

Given x ∈ Z and | x | ≤ 2 Z is a set of integers Integers are … - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , … Now, if we take x = - 3 then we have to check that it satisfies the given condition | x | ≤ 2 | - 3 | = 3 > 2 So, - 3 ∉ H If x = - 2 then | - 2 | = 2 [satisfying | x | ≤ 2 ] So, - 2 ∈ H If x = - 1 then | - 1 | = 1 [satisfying | x | ≤ 2 ] ∴ - 1 ∈ H If x = 0 then | 0 | = 0 [satisfying | x | ≤ 2 ] ∴ 0 ∈ H If x = 1 then | 1 | = 1 [satisfying | x | ≤ 2 ] ⇒ 1 ∈ H If x = 2 then | 2 | = 2 [satisfying | x | ≤ 2 ] So, 2 ∈ H If x = 3 then | 3 | = 3 > 2 [not satisfying | x | ≤ 2 ] So, 3 ∉ H So, H = { - 2 , - 1 , 0 , 1 , 2 }

E M B I B E

Senior Secondary School Mathematics FOR CLASS 11>Set and Functions>Chapter 1 - Sets>EXERCISE 1A

R S Aggarwal Solutions for Exercise 1: EXERCISE 1A

Author:R S Aggarwal

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

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