# Union of the Sets

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