Subset Calculator

The subset calculator determine the total number of proper and improper subsets in the sets. As well, this calculator tells about the subsets with a specific number of elements.

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.

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, which gives the number of the proper and improper subset in a set.

Example:

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.

How to Find the Number of Subsets and Proper Subsets:

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

Example:

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

Solution:

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

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 ⊆.

Example

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 Our Calculator Works?

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

Input:

• 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.

Output:

• 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.

Reference:

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

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