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Subset Calculator

Subset Calculator

Select the method and input numbers in the designated box to calculate all possible proper and improper subsets of the data set, with steps displayed.



Enter set value separated with comma (,):

Enter elements length:

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An online subset calculator allows you to determine the total number of proper and improper subsets in the sets. As well, this calculator tells about the subsets with the specific number of elements. Here we’ll explain subset vs proper subset difference and how to find subsets of a given set.

What is a Subset?

According to subset definition, if all elements of set A also exist in set B, then set A is called a subset of set B. In other words, set A is included in the set.

In mathematics, a subset is represented by the symbol ⊆, and is pronounced “is a subset notation”.

The subset notation can be expressed as P⊆Q

This means that set P is a subset of set Q.

However, an Online Power Set Calculator will be used to generate the power sets of a given set.

Subsets Example:

If set P has {A, B} and set Q has {A, B, C}, then P is a subset of Q because there are also elements of set “P” in set “Q”.

Types of Subsets:

There are two different types of Subset:

  • Proper Subset
  • Improper Subset

A proper subset contains few elements of the original set but an improper subset contains each element of the Original set, as well as an empty set and subset calculator, which gives the number of the proper and improper subset in a set. No specific formula was found for the subset. Instead, we need to list all the subsets to distinguish proper from improper.


If set P = {10, 14, 16}, then,

Number of subsets:

$${10}, {14}, {16}, {10, 14}, {14, 16}, {10, 16}, {10, 14, 16}, {}$$

Proper Subsets:

$${}, {10}, {14}, {16}, {10, 14}, {14, 16}, {10, 16}$$

Improper Subset:

$${10, 14, 16}$$

What is Proper Subset?

If set Q contains at least one element that is not in set P, then set P is considered to be the proper subset of set Q.

The proper subset is a special subset. There are two requirements for set P to become the proper subset of set Q.

  • P is a subset of Q, namely PQ, and P is not equal to Q, that is, P≠Q.
  • Subset notation: P⊂Q: it means set P is the proper subset of the set Q.


If you set P with elements {5, 10} and Q set to {5, 10, 15}, the set P is a valid subset of Q, because 15 does not exist in set P.

Notation for Proper Subset:

The subset notation for the proper subset is denoted as ⊂ and read as “is a proper subset”. Through this symbol, we can represent set P and set Q as a Proper subset:

$$P ⊂ Q$$

However, an online Interval Notation Calculator helps you to find the interval values from the given set interval notation.

How to Find the Number of Subsets and Proper Subsets:

  • If a set has “n” elements, then an online subset calculator uses the number of subsets of a given set as \(2^n\)
  • The number of proper subsets of a given sub-set is \(2^n-1\).


Determine the number of subsets and proper subsets for the set P = {7, 8, 9}.


$$P = {7, 8, 9}$$

So, the number of elements in the set is 3 and the formula for computing the number of subsets of a given set is 2n

$$ 2^3 = 8$$

Hence the number of subsets is 9

Using the formula of proper subsets of a given set is 2n – 1

$$= 2^3 – 1$$

$$= 8 – 1 = 7$$

The number of proper subsets is 7.

What is an improper subset?

Contains a subset of all the elements of the original set. This is called an improper subset.

It is donated as ⊆.


If set Q = {10, 14, 16}, then,

Number of subsets:

$${10}, {14}, {16}, {10, 14}, {14, 16}, {10, 16}, {10, 14, 16}, {}$$

Improper Subset:

$${10, 14, 16}$$

Some Important Attributes of Subsets:

  • Each set is considered a subset of the specified set itself. This means P⊂P or Q⊂Q, and the empty set is considered a subset of all sets.
  • P is a subset of Q. This means that set P is in Q.
  • If set P is a subset of set Q, we can say that Q is a superset of P.

How Subset Calculator Works?

Use this online subsets calculator which helps you to find subsets of a given set by following these instructions:


  • First, select an option which type you want to calculate by such as set elements or cardinality.
  • Now, enter set values and ensure all values are separated with a comma.
  • Click on the “calculate” button for the results.


The subset calculator provides:

  • It displays the values of subsets and proper subsets.
  • The calculator tells how many subsets in elements.
  • It creates a list of subsets if you choose the set elements option.


Is the cardinality of the empty set always zero?

The cardinality of the empty set is the number of elements. The cardinality of the empty set is 0 because the empty set does not contain any elements. In the established symbols, we write |Ø| = 0.

Is pi a proper subset?

The empty set, the pi is a proper subset of any given set that contains at least one element and an inappropriate subset of pi.


Use this online subset calculator which fined the subsets containing the number of elements. Also, determine the numbers of proper and improper subsets. Knowing the number of subsets and elements is such a time-consuming task but thanks to the free subsets calculator that provides the number of elements in every subset.


From the source of Wikipedia: Subset, Proper subset, Superset, Inclusion, Properties, ⊂ and ⊃ symbols.

From the source of Brilliant: Sets – Subsets, Proper Subsets, Subset versus proper subset, the Number of subsets in a Set.

From the source of Proof Wiki: Euler Diagram, Superset, Notation, British People are Subset of People, Subset of Alphabet, Integers are Subset of Real Numbers, Initial Segment is Subset of Integers, Even Numbers form Subset of Integers.

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