Power Set Calculator – Find All Subsets of a Set with Steps
The Power Set Calculator finds every subset of a given set, calculates the total number of subsets, proper subsets, and the cardinality of the power set. Enter elements separated by commas to generate the complete power set instantly with step-by-step calculations.
Calculator
A set is called the power set of any set, if it contains all subsets of that set.
P(S) is the notation for representing any power set of the set.
for example:
for the set S={1,2,3,4,5} means that S has 5
P(S) = 2n = 25 = 32
Frequently Asked Questions
What is a power set?
A power set is the collection of every possible subset of a set, including the empty set and the original set itself.
How many subsets does a set have?
If a set contains n elements, the total number of subsets is calculated using the formula 2n.
What is the difference between a subset and a proper subset?
A subset may be equal to the original set, whereas a proper subset contains fewer elements and is never identical to the original set.
Does the empty set belong to every power set?
Yes. Every power set always contains the empty set (∅), regardless of how many elements are in the original set.
Can this calculator handle letters as well as numbers?
Yes. You can enter numbers, letters, symbols, or words separated by commas, such as A,B,C or apple,banana,orange.
How is the number of proper subsets calculated?
The number of proper subsets is 2n − 1, because the original set itself is excluded.
What is the cardinality of a power set?
The cardinality of a power set is equal to the total number of subsets, which is 2n.
Why is the formula 2n used?
Each element has two choices: it can either be included or excluded from a subset. Therefore, n independent choices produce 2n different subsets.
Can I use this calculator for large sets?
Yes, but remember that the number of subsets grows exponentially. A set with 20 elements already has over one million subsets.
Is this calculator suitable for students?
Yes. It is designed for school, college, and competitive exam preparation, providing formulas and step-by-step explanations.