English

Let a = { ϕ , { ϕ } , 1 , { 1 , ϕ } , 2 } Which of the Following Are True? ϕ ∈ a

Advertisements
Advertisements

Question

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

\[\left\{ \phi \right\} \in A\]

 

Advertisements

Solution

True

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

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 1 Sets
Exercise 1.04 | Q 8.2 | Page 17

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Write the following set in roster form:

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


Write the following set in roster form:

E = The set of all letters in the word TRIGONOMETRY


List all the elements of the following set:

C = {x : x is an integer, x2 ≤ 4}


List all the elements of the following set:

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


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:  

 0 ...... A


Describe the following sets in set-builder form: 

{2, 4, 6, 8 .....}


List all the elements of the following set: 

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


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

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


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

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


Which of the following statement 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? 

\[\left\{ c, d \right\} \in A\] 


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: 

\[1 \in A\] 


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

\[\left\{ 6, 7, 8 \right\} \in A\] 


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


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

 {a


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

{1, 2},


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


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

10 _____ A


Describe the following set in Roster form

A = {x/x is a letter of the word 'MOVEMENT'}


Describe the following set in Set-Builder form

{0}


If A = {x/6x2 + x – 15 = 0}, B = {x/2x2 – 5x – 3 = 0}, C = {x/2x2 – x – 3 = 0} then find (A ∪ B ∪ C).


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.


Answer the following:

Write down the following set in set-builder form

{a, e, i, o, u)


Answer the following:

In a school there are 20 teachers who teach Mathematics or Physics. Of these, 12 teach Mathematics and 4 teach both Physics and Mathematics. How many teachers teach Physics?


Write the following sets in the roaster form:
E = `{w | (w - 2)/(w + 3) = 3, w ∈ R}`


Write the following sets in the roaster form:

F = {x | x4 – 5x2 + 6 = 0, x ∈ R}


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

3 ∉ {x | x4 – 5x3 + 2x2 – 112x + 6 = 0}


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


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 French and Sanskrit but not 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 French and English but not Sanskrit


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 at least one of the three languages


Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis. Then ______.


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 ______.


A survey shows that 63% of the people watch a News Channel whereas 76% watch another channel. If x% of the people watch both channel, then ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×