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Class 11 Maths Chapter 1 Sets Lecture 2

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
  1. 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}
  1. 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}
  1. 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
  1. Write down all the subsets of the following sets
  • {a}
  • {a, b}
  • {1, 2, 3}
  • \phi
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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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