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# Lecture - 2 Chapter 1 Sets

If you don’t stand for something you’ll fall for anything. – Malcolm X

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NCERT EXERCISE 1.3 |

- Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces :
*(i)*{ 2, 3, 4 } . . . { 1, 2, 3, 4,5 }- {
*a*,*b*,*c*} . . . {*b*,*c*,*d*} - {
*x*:*x*is a student of Class XI of your school}. . .{*x*:*x*student of your school} - {
*x*:*x*is a circle in the plane} . . .{*x*:*x*is a circle in the same plane with radius 1 unit} *(v)*{*x*:*x*is a triangle in a plane} . . . {*x*:*x*is a rectangle in the plane}- {
*x*:*x*is an equilateral triangle in a plane} . . . {*x*:*x*is a triangle in the same plane} - {
*x*:*x*is an even natural number} . . . {*x*:*x*is an integer}

- Examine whether the following statements are true or false:
*(i)*{*a*,*b*} ⊄ {*b*,*c*,*a*}- {
*a*,*e*} ⊂ {*x*:*x*is a vowel in the English alphabet} - { 1, 2, 3 } ⊂ { 1, 3, 5 }
- {
*a*}⊂ {*a*,*b*,*c*} *(v)*{*a*}∈ {*a*,*b*,*c*}- {
*x*:*x*is an even natural number less than 6} ⊂ {*x*:*x*is a natural number which divides 36}

- Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

*(i)*{3, 4} ⊂ A- {3, 4} ∈ A
- {{3, 4}} ⊂ A
- 1 ∈ A
*(v)*1 ⊂ A- {1, 2, 5} ⊂ A
- {1, 2, 5} ∈ A
- {1, 2, 3} ⊂ A
- f ∈ A
*(x)*f ⊂ A- {f} ⊂ A

- Write down all the subsets of the following sets

- {
*a*} - {
*a*,*b*} - {1, 2, 3}
- \( \phi \)

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##### Clip - 1

5. How many elements has P(A), if A = f?

6. Write the following as intervals :

*(i)*{*x*:*x*∈**R**, – 4 <*x*≤ 6}- {
*x*:*x*∈**R**, – 12 <*x*< –10} - {
*x*:*x*∈**R**, 0 ≤*x*< 7} - {
*x*:*x*∈**R**, 3 ≤*x*≤ 4}

7. Write the following intervals in set-builder form:

*(i)*(– 3, 0)- [6, 12]
- (6, 12]
- [–23, 5)

8. What universal set(s) would you propose for each of the following:

*(i)*The set of right triangles.- The set of isosceles triangles.

9. Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and C

*(i)*{0, 1, 2, 3, 4, 5, 6}- \( \phi \)
- {0,1,2,3,4,5,6,7,8,9,10}
- {1,2,3,4,5,6,7,8}

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