Reply To: Types of sets

Sets are nothing but a collection or arrangement of distinct elements. They are classified into many categories.

Let's discuss some of them:

This type of set contains only a particular number of elements.

Example: S = { x | x ∈ N and 100> x > 30 }

This type of set contains an infinite number of elements.

Example: S = { y | y ∈ N and y > 0 }

If there are two sets such as Set A and Set B. And if further every element of A is an element of set B then we call A to be a subset of set B

Example: − Let, B= { 0, 1, 2, 3, 7, 8, 9} and A= { 8, 9}. So, above A is a subset of set B as all the elements of set A are present in set B.

If there are two sets such as Set A and Set B. A Set A is a proper subset of set B if and only if every element of A is an element of set B.

Example − Let, A= { 1, 2, 3, 4, 5, 6 } and B= { 1, 2 }.

A universal set is a set that contains all elements of the particular criteria. Hence all the sets from that area are subsets of this universal set. It is represented by U.

Example: The set of all plants on earth be U. So, the set of all cactus is a subset of U.

A set which have no elements is known as Empty Set.

Example: S = { a| a ∈ N and 15< a< 14} = ∅

A set which has only one element in it is called singleton set.

Example: S = { x | x ∈ N, 15> x > 13} = { 14}

If two sets have the exact same elements then they are known as equal sets.

Example: If A = { 12, 13, 14, 15, 17 } and B = { 17, 13, 12, 15, 14 }

Then they are equal sets

If the number of elements of two sets are equal, then they are known as equivalent sets.

Example: If A = { 0, 5, 2, 6 } and B = { 12, ,3 17, 92 }

Then they are equivalent sets.

If two sets contain one same element then they are known as overlapping sets.

Example: X = { 11, 12, 61 } and Y= { 100, 12, 4 }. So, here is one common element ‘12’. Therefore, they are overlapping sets.

If there are two sets A and B. And if they have no common elements then they are known as disjoint sets.

Example: X= { 1, 3, 6 } and Y= { 17, 900, 124 }. No common elements are there so they are disjoint sets.