Types of Sets

We know that a set is a well–defined collection of objects. There are different types of sets depending on the objects and their characteristics. Let us understand the various types of sets along with illustrations.

1. Empty Set or Null set:

It has no element present in it. Example: A = {} is a null set.

2. Unit or Singleton Set:

3. Finite Set:

It has a limited number of elements. Example: A = {1,2,3,4}

4. Infinite Set: 

It has an infinite (uncountable) number of elements. Example: A = {x: x is the set of all whole numbers}

5. Equal Set: 

Two sets that have the same members. Example: A = {1,2,5} and B={2,5,1}: Set A = Set B

6. Equivalent Set:

If the cardinalities (number of elements) of two sets are the same, they are called equivalent sets.

Example: If A = { 1, 2, 6 } and B = { 16, 17, 22 }, they are equivalent as cardinality of A is equal to the cardinality of B. i.e. |A| = |B| = 3

7. Overlapping Set:

Two sets that have at least one common (same) element are called overlapping sets.

Example: Let, A = { 1, 2, 6 } and B = { 6, 12, 42 }. There is a common element ‘6’, hence these sets are overlapping sets.

8. Disjoint Set:

Two sets A and B are called disjoint sets if they do not have any element in common.

Example: Let, A = { 1, 2, 6 } and B = { 7, 9, 14 }, there is not a single common element, hence these sets are overlapping sets.