Subset Calculator
Understanding Subsets
This calculator has two modes for working with subsets.
1. Generate Subsets of a Specific Size
This mode lists all possible subsets of a specific size 'k' from a larger set of 'n' elements. The total number of such subsets is calculated using the combination formula:
\[ C(n, k) = \binom{n}{k} = \frac{n!}{k!(n-k)!} \]
2. Analyze Subsets by Cardinality
This mode takes the size of a set (its cardinality, 'n') and provides a full breakdown of its power set (the set of all possible subsets).
- Total Subsets: A set with 'n' elements has \(2^n\) total subsets.
- Proper Subsets: These are all subsets except the set itself. There are \(2^n - 1\) proper subsets.
The calculator shows how many subsets exist for each possible size from 0 to n.
Finds all subsets of size 'k' from a set 'n'.
Analyzes the subset distribution for a set of size 'n'.
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