# 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}
• $$\phi$$
##### Clip - 1

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

6. Write the following as intervals :

• (i) {x : xR, – 4 < x ≤ 6}
• {x : xR, – 12 < x < –10}
• {x : xR, 0 ≤ x < 7}
• {x : xR, 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}