Short Answer Type
{x : x is a vowel in the English alphabet}
What universal set(s) would you propose for each of the following?
(i) The set of right triangles, (ii) The set of isosceles triangles.
Write down all the subsets of the following sets
(i) {a} (ii) {a, b} (iii) {1, 2, 3} (iv) φ
(a) A = {a}
Number of elements in set A = 1
Number of subsets = 21 = 2
∴ The subsets are φ, {a}
(b) A = {a, b}
Number of elements in set A = 2
Number of subsets = 22 = 4
∴ The subsets are φ, {a}, {b}, {a, b}
(c) A = {1, 2, 3}
Number of elements in set A = 3
Number of subsets = 23 = 8
∴ The subsets are φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3} and {1, 2, 3}
(d) φ = { }
Number of elements = 0
Number of subsets = 20 = 1
∴ The subsets is φ
Given sets A = {1, 3, 5}, B = {2, 4, 6}, C = {0, 2, 4, 6, 8}, which of the following can be considered as universal set(s) of three sets A, B, C ?
(i) {0,1,2,3,4,5,6} (iii)ϕ
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10} (iv) {1, 2, 3, 4, 5, 6, 7, 8}
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)-∞ 31 (ii) (-∞, 0) (iii) [-1, ∞) (iv) (3, ∞)
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