Definition of Union of Sets:
Union of two given sets is the smallest set which contains all the elements of both the sets.
To find the union of two given sets A and B is a set which consists of all the elements of A and all the elements of B such that no element is repeated.
The symbol for
denoting union of sets is ‘∪’.
For example;
Let
set A = {2, 4, 5, 6}
and set B = {4, 6, 7, 8}
Taking every element of both the sets A and B, without repeating any element, we get a new set = {2, 4, 5, 6, 7, 8}
This new set contains all the elements of set A and all the elements of set B with no repetition of elements and is named as union of set A and B.
The symbol used for the union of two sets is ‘∪’.
Therefore,
symbolically, we write
union of the two sets A and B is A ∪ B which means A union B.
Therefore, A ∪ B = {x : x ∈ A or x ∈ B}
Solved examples to find union of two given sets:
1. If A = {1, 3, 7, 5} and B = {3, 7, 8, 9}. Find union of two set A and B.
Solution:
A ∪ B = {1, 3, 5, 7, 8, 9}
No element is repeated in the union of two sets.
The common elements 3, 7 are taken only once.
2. Let X = {a, e, i, o, u} and Y = {ф}. Find union of two given sets X and Y.
Solution:
X ∪ Y = {a, e,
i, o, u}
Therefore,
union of any set with an empty set is the set itself.
3. If set P = {2, 3, 4, 5, 6, 7}, set Q = {0, 3, 6, 9, 12} and set R = {2, 4, 6, 8}.
(i) Find the union of sets P and Q
(ii) Find the union of two set P and R
(iii) Find the union of the given sets Q and R
Solution:
(i) Union of sets P and Q is P ∪ Q
The smallest set which contains all the elements of set P and all the elements of set Q is {0, 2, 3, 4, 5, 6, 7, 9, 12}.
(ii) Union of two set P and R is P ∪ R
The smallest set which contains all the elements of set P and all the elements of set R is {2, 3, 4, 5, 6, 7, 8}.
(iii) Union of the given sets Q and R is Q ∪ R
The smallest set which contains all the elements of set Q and all the elements of set R is {0, 2, 3, 4, 6, 8, 9, 12}.
Notes:
A and B are the
subsets of A ∪ B
The union of sets is commutative, i.e., A ∪ B = B ∪ A.
The operations are performed when the sets are
expressed in roster form.
Some properties of the operation of union:
(i) A∪B = B∪A (Commutative law)
(ii) A∪(B∪C) = (A∪B)∪C
(Associative law)
(iii) A ∪ ϕ = A (Law of identity element, is the
identity of ∪)
(iv) A∪A = A
(Idempotent law)
(v) U∪A = U
(Law of ∪) ∪ is the universal set.
Notes:
A ∪ ϕ = ϕ ∪ A = A i.e. union of any set with the empty set is always the set itself.
● Set Theory
● Sets
● Subset
7th Grade Math Problems
From Definition of Union of Sets to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.