English

List All the Elements of the Following Sets: a = { X : X 2 ≤ 10 , X ∈ Z }

Advertisements
Advertisements

Question

List all the elements of the following sets: 

\[A = \left\{ x: x^2 \leq 10, x \in Z \right\}\] 

Advertisements

Solution

\[ A = {0, \pm 1, \pm 2, \pm 3}\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Sets - Exercise 1.02 [Page 6]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 1 Sets
Exercise 1.02 | Q 3.1 | Page 6

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Write the following set in roster form:

B = {x : x is a natural number less than 6}


Write the following set in roster form:

E = The set of all letters in the word TRIGONOMETRY


Write the following set in the set-builder form:

{3, 6, 9, 12}


Write the following set in the set-builder form:

{2, 4, 8, 16, 32}


Write the following set in the set-builder form:

{2, 4, 6, …}


List all the elements of the following set:

A = {x : x is an odd natural number}


List all the elements of the following set:

F = {x : x is a consonant in the English alphabet which precedes k}.


Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

(i) {1, 2, 3, 6} (a) {x : x is a prime number and a divisor of 6}
(ii) {2, 3} (b) {x : x is an odd natural number less than 10}
(iii) {M, A, T, H, E, I, C, S} (c) {x : x is natural number and divisor of 6}
(iv) {1, 3, 5, 7, 9} (d) {x : x is a letter of the word MATHEMATICS}

If A = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], then insert the appropriate symbol ∈ or ∉ in each of the following blank space: 

−4 ...... A 


If A = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], then insert the appropriate symbol ∈ or ∉ in each of the following blank space: 

 9 ...... A


If A = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], then insert the appropriate symbol ∈ or ∉ in each of the following blank space:  

 0 ...... A


If A = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], then insert the appropriate symbol ∈ or ∉ in each of the following blank space: 

−2 ...... A


Describe the following sets in Roster form: 

{x : x is a letter before e in the English alphabet}


Describe the following sets in Roster form: 

{x ∈ N : x2 < 25}; 


Describe the following sets in Roster form: 

 {x ∈ N : x = 2nn ∈ N};


Describe the following set in Roster form: 

The set of all letters in the word 'Trigonometry'


Describe the following sets in set-builder form: 

E = {0}


Write the set \[\left\{ \frac{1}{2}, \frac{2}{5}, \frac{3}{10}, \frac{4}{17}, \frac{5}{26}, \frac{6}{37}, \frac{7}{50} \right\}\]  in the set-builder form.


Which of the following statement are correct?
Write a correct form of each of the incorrect statements.  

\[a \subset \left\{ a, b, c \right\}\] 


Let A = {ab, {cd}, e}. Which of the following statement are false and why? 

\[\left\{ \left\{ c, d \right\} \right\} \subset A\]


Let A = {ab, {cd}, e}. Which of the following statement are false and why? 

\[\phi \in A\]


Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false: 

\[\left\{ 1, 2, 3 \right\} \subset A\] 

 


Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true? \[\left\{ 1 \right\} \in A\]

 


Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[2 \subset A\]


What is the total number of proper subsets of a set consisting of n elements? 


If A is any set, prove that: \[A \subseteq \phi \Leftrightarrow A = \phi .\] 


Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:

0 ____ A


Describe the following set in Roster form

B = `{x//x  "is an integer", -3/2 < x < 9/2}`


Describe the following set in Roster form

C = {x/x = 2n + 1, n ∈ N}


In a hostel, 25 students take tea, 20 students take coffee, 15 students take milk, 10 students take bot tea and coffee, 8 students take both milk and coffee. None of them take tea and milk both and everyone takes at least one beverage, find the total number of students in the hostel.


Write the following interval in Set-Builder form

`(-∞, 5]`


Write the following interval in Set-Builder form

[– 3, 4)


Answer the following:

Write down the following set in set-builder form

{a, e, i, o, u)


Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:
n + 5 = 8


Write the following sets in the roaster from:
C = {x | x is a positive factor of a prime number p}


State which of the following statements is true and which is false. Justify your answer.

496 ∉ {y | the sum of all the positive factors of y is 2y}.


Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed in Mathematics only


Let F1 be the set of parallelograms, F2 the set of rectangles, F3 the set of rhombuses, F4 the set of squares and F5 the set of trapeziums in a plane. Then F1 may be equal to ______.


If A and B are any two sets, then A – B is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×