# Union of the Sets

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

The set consisting of all elements of the set A and set B is called the union of the sets A and B. It is denoted by A ∪ B. ( Read as A union B). Properties on union of the sets

1) A ∪ A = A

2) A ∪ φ = A

3) A ∪ B = B ∪ A (Commutative property for union)

4) ( A ∪ B ) ∪ C = A ∪ ( B ∪ C ) ( Associative property )

5) U ∪ A = U (Law of U)

Examples :

1) If A = { 1, 2, 3, 4} and B = { 2, 3, 5, 6, 7 } then find A ∪ B.

Solution :
A = { 1, 2, 3, 4} and B = { 2, 3, 5, 6, 7 }

A union B is obtained by combining the two sets but if there is any element which is common in both taken only once.

∴ A ∪ B = { 1, 2, 3, 4, 5, 6, 7 }

2) If P = { 1, 2, 3, 4 } and Q = { x | x ∉ N, 1 < x < 8 } then find P ∪ Q.

Solution :
P = { 1, 2, 3, 4 }

Q = { x | x ∉ N, 1 < x < 8 }

Q = { 2, 3, 4, 5, 6, 7 }

∴ P ∪ Q = { 1, 2, 3, 4, 5, 6, 7 }.

3) If A = { x | x is a multiple of 2 } and
B = { x | x is an odd natural number }. Find A ∪ B.

Solution :
A = { x | x is a multiple of 2 }

A = { 2, 4, 6, 8, 10, … }

B = { x | x is an odd natural number }.

B = { 1, 3, 5, 7, 9,11, … }

∴ A ∪ B = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, … }
Set Theory

Sets
Representation of Set
Cardinal Number
Types of Sets
Pairs of Sets
Subset
Complement of Set
Union of the Sets
Intersection of Sets
Operations on Sets
De Morgan's Law
Venn Diagrams
Venn-diagrams for sets
Venn-diagrams for different situations
Problems on Intersection of Two Sets
Problems on Intersection of Three Sets