Subset Calculator

Use this Subset Calculator to Find all the Proper and Improper Subsets of the Given Data Set.

Subset Finder

Summary

Total Subsets

Proper Subsets

All Subsets

Cardinality Distribution

Number of Subsets	Elements Count

What is a Subset?

In mathematics, a set A is a subset of set B if all elements of A are also elements of B. B is then a superset of A. For example, if set A = {1, 2, 3} and set B = {1, 2, 3, 4, 5} then, we can say that set A is a subset of set B since all the elements in set A are present in set B.

The total number of subsets of a set with 'n' elements is 2ⁿ.

Subset Symbols

There are two subset symbols:

⊆, which is read as "is a subset or equal to" (A ⊆ B)
⊂, which is read as "is a subset of" (A ⊂ B)

Types of Subsets

There are two types of subsets:

Proper subset (⊂ is used)
Improper Subset (⊆ is used)

Subset Finder

combinationsumcalculator.pro

{1, 2, 3}

{1, 2, 4}

{1, 3, 4}

{2, 3, 4}

{1, 2, 5}

{2, 3, 5}

{1, 4, 5}

{2, 4, 5}

{3, 4, 5}

{1, 2, 3, 4}

{1, 2, 3, 5}

{1, 2, 4, 5}

Types of Subsets

1

Proper Subset

A set A is a proper subset of set B if every element of A is in B and A ≠ B (they are not equal). It is represented as A ⊂ B.

The number of proper subsets of a set with 'n' elements is 2ⁿ-1.

A proper subset is any subset of the set except itself. For example,

A = {1, 2} and B = {1, 2, 3}
Here, A ⊂ B because all of A's elements are in B but A ≠ B.

2

Improper Subset

A set A is an improper subset of B if A = B.

An improper subset is a subset of the set which is not a propet subset.

The number of improper subsets of a set with 'n' elements is always 1.

A = {1, 2, 3} and B = {1, 2, 3}
If A is an improper subset of B, then A ⊆ B (A = B).

How to Calculate Total Number of Subsets?

If a set A has 'n' elements, then the total number of subsets of A is calculated using the formula 2ⁿ.

Similarly, if a set A has 'n' elements, then the total number of proper subsets of A is calculated using the formula 2ⁿ-1.

Total Subsets

If set A = {1, 2, 3, 4, 5}, then this set has n = 5 elements. Thus, we will use the 2ⁿ formula to find all the subsets of the given set A = 2⁵ = 32.

Thus, set A has 32 subsets = {}, {1}, {2}, {1, 2}, {3}, {1, 3}, {2, 3}, {1, 2, 3}, {4}, {1, 4}, {2, 4}, {1, 2, 4}, {3, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}, {5}, {1, 5}, {2, 5}, {1, 2, 5}, {3, 5}, {1, 3, 5}, {2, 3, 5}, {1, 2, 3, 5}, {4, 5}, {1, 4, 5}, {2, 4, 5}, {1, 2, 4, 5}, {3, 4, 5}, {1, 3, 4, 5}, {2, 3, 4, 5}, {1, 2, 3, 4, 5}.

Proper Subsets

If set B = {2, 4, 6, 8}, then using proper subset formula, we'll get: Total Proper Subsets = 2ⁿ-1 = 2⁴-1 = 16-1 = 15 proper subsets.

Thus, set B has 15 proper subsets = {}, {2}, {4}, {2, 4}, {6}, {2, 6}, {4, 6}, {2, 4, 6}, {8}, {2, 8}, {4, 8}, {2, 4, 8}, {6, 8}, {2, 6, 8}, {4, 6, 8}.