problem archive
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Consider the sets ϕ, A = {1, 3}, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}. Insert the symbol ⊂ or ⊄ between each of the following pair of sets: (i) ϕ . . . ... -
Let A = {a, e, i, o, u} and B = {a, b, c, d}. Is A a subset of B? No. (Why?). Is B a subset of A? No. (Why?) -
Let A, B and C be three sets. If A ⊆ B and B ⊆ C, is it true that A ⊆ C?. If not, give an example. -
If A = (-3, 5) and B = [-7, 9], then A ⊂ B. -
The set {x : x ∈ R, -5 < x ≤ 7}, written in set-builder form, can be written in the form of interval as (-5, 7] and the interval [-3, 5) can be writte... -
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:... -
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... -
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... -
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 se... -
Let A = {2, 4, 6, 8} and B = {6, 8, 10, 12}. Find A ∪ B. -
Let A = {a, e, i, o, u} and B = {a, i, u}. Show that A ∪ B = A. -
Let X = {Ram, Geeta, Akbar} be the set of students of Class XI, who are in school hockey team. Let Y = {Geeta, David, Ashok} be the set of students fr... -
Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = {2, 3, 5, 7}. Find A ∩ B and hence show that A ∩ B = B. -
Let A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8}. Find A - B and B - A -
1. Find the union of each of the following pairs of sets: (i) X = {1, 3, 5} Y = {1, 2, 3} (ii) A = {a, e, i, o, u} B = {a, b, c} (iii) A = {x: x is a ... -
2. Let A = {a, b}, B = {a, b, c}. Is A ⊆ B? What is A ∪ B?