English

Let a = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine Which of the Following is True Or False: ϕ ∈ a - Mathematics

Advertisements
Advertisements

Question

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

\[\phi \in A\] 

Solution

True 

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Sets - Exercise 1.04 [Page 17]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 1 Sets
Exercise 1.04 | Q 7.6 | Page 17

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Identify whether the following is set or not? Justify your answer.

The collection of ten most talented writers of India.


Identify whether the following is set or not? Justify your answer.

The collection of all boys in your class.


Write the following set in roster form:

A = {x : x is an integer and –3 ≤ x < 7}


Write the following set in the set-builder form:

{3, 6, 9, 12}


Write the following set in the set-builder form:

{5, 25, 125, 625}


Write the following set in the set-builder form:

{2, 4, 6, …}


List all the elements of the following set:

B = `{x : x  "is an integer", -1/2 < x < 9/2}`


List all the elements of the following set:

E = {x : x is a month of a year not having 31 days}


Which of the following collection are sets? Justify your answer: 

 The collection of difficult topics in 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: 

12 ...... A


Describe the following sets in Roster form: 

 {x ∈ R : x > x}.


Describe the following sets in set-builder form: 

{1, 4, 9, 16, ..., 100} 


Describe the following sets in set-builder form: 

{5, 25, 125 625} 


List all the elements of the following set: 

\[B = \left\{ x: x = \frac{1}{2n - 1}, 1 \leq n \leq 5 \right\}\]


List all the elements of the following set: 

\[C = \left\{ x: x \text{ is an integer }, - \frac{1}{2} < x < \frac{9}{2} \right\}\]


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

(i) {APLE} (i) x : x + 5 = 5, x ∈ Z
(ii) {5, −5} (ii) {x : x is a prime natural number and a divisor of 10}
(iii) {0} (iii) {x : x is a letter of the word "RAJASTHAN"}
(iv) {1, 2, 5, 10,} (iv) {xx is a natural number and divisor of 10}
(v) {AHJRSTN} (v) x : x2 − 25 = 0
(vi) {2, 5} (vi) {x : x is a letter of the word "APPLE"}

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

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


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

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


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

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


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

\[\left\{ a, b, e \right\} \in A\] 


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? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\] 


Write down all possible subsets of each of the following set: 

 {0, 1}, 


Write down all possible proper subsets each of the following set: 

{1}. 


Describe the following set in Set-Builder form

{0}


Write the following interval in Set-Builder form:

[6, 12]


Write the following interval in Set-Builder form

`(-∞, 5]`


A college awarded 38 medals in volleyball, 15 in football, and 20 in basketball. The medals awarded to a total of 58 players and only 3 players got medals in all three sports. How many received medals in exactly two of the three sports?


Answer the following:

Write down the following set in set-builder form

{10, 20, 30, 40, 50}


State which of the following statement are true and which are false. Justify your answer.

7,747 ∈ {t | t is a multiple of 37}


Given that E = {2, 4, 6, 8, 10}. If n represents any member of E, then, write the following sets containing all numbers represented by n2 


Write the following sets in the roaster from:
B = {x | x2 = x, x ∈ R}


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 English and Mathematics but not in Science.


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 and Science but not in English


In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows:
French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study Sanskrit only


In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Then, the number of students who play neither is ______.


State True or False for the following statement.

Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×