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
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}
Consider U1 = {0, 1, 2, 3, 4, 5, 6}
∴ U1 is not a universal set for A, B, C.
Consider : U2 = 
None of members of sets A, B, C are members of set U2
∴ U2 is not a universal set.
Consider : U3 = {0, 1, 3, 4, 5, 6, 7, 8, 9, 10}
Every member of sets A, B and C is a member of set U3.
Hence U3 = {0, 1, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set for sets A, B, C.
Consider U4 = {1, 2, 3, 4, 5, 6, 7, 8 }
∴ U4 is not a universal set sets A, B and C.
Hence, the universal set is U3 = {0, 1, 3, 4, 5, 6, 7, 8, 9, 10}
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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