Sets
Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : (i) { 2, 3, 4 } . . . { 1, 2, 3, 4,5 } (ii) { a, b, c } . . . { b, c, d } (iii) {x : x is a student of Class XI of your school}. . .{x : x student of your school} (iv) {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} (vi) {x : x is an equilateral triangle in a plane} . . . {x : x is a triangle in the same plane} (vii) {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 } (ii) { a, e } ⊂ { x : x is a vowel in the English alphabet} (iii) { 1, 2, 3 } ⊂ { 1, 3, 5 } (iv) { a } ⊂ { a, b, c } (v) { a } ∈ { a, b, c } (vi) { 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 (ii) {3, 4} ∈ A (iii) {{3, 4}} ⊂ A (iv) 1 ∈ A (v) 1 ⊂ A (vi) {1, 2, 5} ⊂ A (vii) {1, 2, 5} ∈ A (viii) {1, 2, 3} ⊂ A (ix) φ ∈ A (x) φ ⊂ A (xi) {φ} ⊂ A
Write down all the subsets of the following sets (i) {a} (ii) {a, b} (iii) {1, 2, 3} (iv) φ
Write the following as intervals : (i) {x : x ∈ R, - 4 < x ≤ 6} (ii) {x : x ∈ R, - 12 < x < -10} (iii) { x : x ∈ R, 0 ≤ x < 7} (iv) {x : x ∈ R, 3 ≤ x ≤ 4}
Write the following intervals in set-builder form : (i) (- 3, 0) (ii) [6 , 12] (iii) (6, 12] (iv) [-23, 5)
What universal set(s) would you propose for each of the following : (i) The set of right triangles. (ii) The set of isosceles triangles.
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} (ii) φ (iii) {0,1,2,3,4,5,6,7,8,9,10} (iv) {1,2,3,4,5,6,7,8}