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Power Set Calculator

Power Set Calculator

Enter set value separated with comma (,):

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An online power set calculator will be used to generate the power sets of a given set. The powerset calculator shows how many methods are available for a set that can be joined without any concern for the order of the subsets. Let’s take a look at the cardinality of a power set with some examples.

What is a Power Set?

In mathematics, the power set is defined as the set of all subsets including the null set and the original set itself. It is donated by P(X). In simple words, this is the set of the combination of all subsets including an empty set of a given set.

For instance, X = {a,b,c} is a set,

Then all subsets {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c} are the element of powerset, such as:

Power set of X, P(X) = {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}.

Where P(X) denotes the powerset.

Power Set Calculator

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

How to Find the Power Sets?

If the set has n elements, then its power set will hold 2n elements. It also provides the cardinality of the power set.

Power Set Example:

Assumes a set X is = {1, 2, 3, 4}

n = Number of elements = 4

Therefore, according the power set calculator elements are 2^4 = 16

$${} null or empty set$$

$${1}, {2}, {3}, {4}$$

$${1, 2}, {1, 3}, {2, 3}, {1, 4}, {2, 4}, {3, 4}$$

$${1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}$$

$${1, 2, 3, 4}$$

Notation:

Generally, the number of digits of a power set can be written as |X|, if X has n values then:

$$|P(X)| = 2^n$$

Properties of Notation:

  • Its value is greater than the original set.
  • The number of elements in a power set of X is 2n, where n is the number of subsets in set X
  • The set and subsets of a finite set are countable.

However, An Online Quartile Calculator helps to calculate the first quartile, second quartile, & interquartile range from the data set.

Null Set:

A null set has no element. Therefore, the power set of a null set { }, can be mentioned as;

  • A set containing an empty set.
  • It contains zero elements.
  • The null set is the only subset.

Recursive Algorithm:

A recursive algorithm is used to create the power sets P(X) of a finite set X.

The operation F (m, L) is defined as

$$F (m, L) = {X ∪ {m} | X ∈ L}$$

It gives the set X in L that has the element m.

If Set X = { }, then P(X) = { { } } is returned.

If m is an element in Set X, L = S {m} such that X {m} forms the complement of the element e in set n, the power set is created by the following algorithm:

$$P(S) = P(L) ∪ F ( m, P(X))$$

How Power Set Calculator Works?

The power set generator is free to use that quickly creates all possible subsets of a given set. Here are some instructions to find the elements and power sets:

Input:

  • First of all, enter the elements of the sets and ensure all the values are separated with a comma.
  • Press the calculate button for sets and subsets.

Output:

  • The power set calculator displays the power sets of entered values.
  • It also tells possible subsets of a certain function.

FAQ:

Can a power set be null or empty?

The power set must contain at least one number. The subset of empty set is \(2^0 = 1\). It is the smallest powerset and proper subset of every powerset.

What is the recursive algorithm?

A recursive algorithm calls itself with smaller input values and acquires the result for the present input by applying simple operations to the return elements for the smaller input.

Is a null set is an infinite set or a finite set?

The null set is considered as a finite set, and its cardinality value is 0.

Final Words:

Use this online power set calculator which counts the number of proper powersets based on the number of elements, as well as finds the total number of subsets. These power sets play a significant role in statistics whenever you required to determine the probability of a particular event. The power set solver quickly displays the number of sets with all possible cardinalities in a fraction of a second.

Reference:

From the source of Wikipedia: Power set, subsets as functions, Relation to binomial theorem, Recursive definition, Subsets of limited cardinality, Power object.

From the source of LibreText: Power Set Operation, Uniqueness, Effectiveness, Variants, Montgomery division.

From the source of nLab: Foundational status, Axiom (power sets), Properties, Cantor’s theorem.