Find the union of each of the following pairs of sets

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 natural number and multiple of 3} B = {x: x is a natural number less than 6}
(iv) A = {x: x is a natural number and 1 < x ≤ 6} B = {x: x is a natural number and 6 < x < 10}
(v) A = {1, 2, 3}, B = Φ
Answer
In Union we write all elements of both sets without repeating.
(i) X = {1, 3, 5} Y = {1, 2, 3} so X ∪ Y= {1, 2, 3, 5}
(ii) A = {a, e, i, o, u} B = {a, b, c} so A∪ B = {a, b, c, e, i, o, u}
(iii) Natural number and multiple of 3 are 3, 6, 9 …
Natural number less than 6 are {1, 2, 3, 4, 5, 6}
So we can write A ∪ B as {1, 2, 4, 5, 3, 6, 9, 12 …}
Hence, A ∪ B = {x: x = 1, 2, 4, 5 or a multiple of 3}
(iv) Natural numbers grater than 1 and lower than and equal to 6 are 2, 3, 4, 5 and 6.
Natural number greater than 6 and less than 10 are 7, 8 and 9.
So that A∪ B = {2, 3, 4, 5, 6, 7, 8, 9}
Hence, A∪ B = {x: x ∈ N and 1 < x < 10}
(v) A = {1, 2, 3}, B = Φ B is a empty set and can be written as B= { } so that A∪ B = {1, 2, 3}