Union of the Sets

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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, … }

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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
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