Find the union of each of the following pairs of sets:
X = {1, 3, 5}; Y = {1, 2, 3}
X ∪ Y = {1, 2, 3, 5}
A = {a, e, i, o, u}; B = {a, b, c}
A ∪ B = {a, b, c, e, i, o, u}
A = {x : x is a natural number and multiple of 3}; B = {x : x is a natural number less than 6}
A ∪ B = {1, 2, 3, 4, 5, 6, 9, 12, 15, ...}
A = {x : x is a natural number and 1 < x 6}; B = {x : x is a natural number and 6 < x < 10}
A ∪ B = {2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 3}; B = φ
A ∪ B = {1, 2, 3}
Explanation
The union of two sets A and B is defined as the set consisting of all elements which are either in A or in B, with common elements taken only once. This is represented symbolically as A ∪ B = {x : x ∈ A or x ∈ B}. For part (v), the property A ∪ φ = A from the textbook is applied, showing that the empty set is the identity element for union.