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)

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

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.

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.

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, … }

• 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

BYJU'S

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers