If you don’t stand for something you’ll fall for anything. – Malcolm X
| 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}
- \( \phi \)
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}