Union of sets : The union of two sets P and Q is the set of all the elements which belong to either P or Q or both.
The symbol for ‘union of ’ is ‘∪’.
Thus P ∪ Q = {x : either x ∈ P or x ∈ Q}
Ex. P = { 4, 6, 8, 16}, Q = { 1, 4, 9, 16}
Then P ∪ Q = { 1, 4, 6, 8, 9, 16}
Properties of Union of Sets
(i) If A is any set, then
(a) A ∪ φ = A (b) A ∪ ξ = ξ (c) A ∪ A = A (d) A ∪ A′ = ξ
(ii) If A, B and C are any sets, then
(a) A ∪ B = B ∪ A (Commutative law) (b) (A ∪ B) ∪ C = A ∪ (B ∪ C) (Associative law) (c) A ⊆ A ∪ B and B ⊆ A ∪ B (d) If A ⊆ B, then A ∪ B = B
Venn diagrams illustrating union of sets
The shaded portions in the following diagrams illustrate the union of given sets.
