Math Calculators ▶ Power Set Calculator
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This 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.
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.
However, an online Interval Notation Calculator helps you to find the interval values from the given set interval notation.
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
$${} null or empty set$$
$${1}, {2}, {3}, {4}$$
$${1, 2}, {1, 3}, {2, 3}, {1, 4}, {2, 4}, {3, 4}$$
$${1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}$$
$${1, 2, 3, 4}$$
Generally, the number of digits of a power set can be written as |X|, if X has n values then:
$$|P(X)| = 2^n$$
A null set has no element. Therefore, the power set of a null set { }, can be mentioned as;
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:
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.
The null set is considered as a finite set, and its cardinality value is 0.
From the source of Wikipedia: Power set, subsets as functions, Relation to binomial theorem, Recursive definition, Subsets of limited cardinality, Power object.