Python Program to Find the Power Set of a Given Set

The power set of a given set \( \mathcal{S} \) is the set of all possible subsets of \( \mathcal{S} \), including: 1) the empty set \(\emptyset \), 2) each individual element of \( \mathcal{S} \) as a subset, 3) all possible combinations of elements in \( \mathcal{S} \), and 4) the set itself \( \mathcal{S} \).

The formula for the Number of Subsets

If a set contains n elements, then the total number of subsets in its power set is given by: \(2^n\)

Example:

If \( \mathcal{S} = \{a,b,c\} \), then the power set \( P(\mathcal{S}) \) is:
\[ P(\mathcal{S}) = \{\emptyset, \{a\}, \{b\}, \{c\}, \{a,b\}, \{a,c\}, \{b,c\}, \{a,b,c\}\} \]

Since \( \mathcal{S} \) has 3 elements, the number of subsets in its power set is: \(2^3\) = 8.

The only subset of an empty set \(\emptyset \) is itself, so its power set is: \(\{\emptyset\} \)

Power Set in Python

If you want to generate a power set programmatically, Python provides an easy way to do so using the itertools module. Here is how you can generate the power set of a set in Python:

from itertools import combinations
import argparse

def power_set(s):
    """
    Find the power set of a given set.
    """
    power_set_result = []
    for r in range(len(s) + 1):
        power_set_result.extend(combinations(s, r))
    return [set(subset) for subset in power_set_result]


def main():
    """
    This program finds power set of a given set
    """
    # provide the set as command-line argument
    parser = argparse.ArgumentParser(description="Find power set")
    parser.add_argument("vals", nargs="*", help="List of values to add to the set")
    args = parser.parse_args()

    # create list using command-line values
    input_set = set(args.vals)

    # find power set
    ps = power_set(input_set)
    print(f"Power set of {input_set}: {ps}")
    print(f"Number of subsets in the power set: {len(ps)}")

if __name__ == "__main__":
    main()

To run this code, save it as power_set.py (or any preferred name you like) and execute it from the command line with space-separated values, as shown below:

python power_set.py 1 2 3 4 5

The code will take all command-line arguments and create a set from them. In this example, the set will be {1, 2, 3, 4, 5}.

Please let me know in the comments if you encounter any issues with the code.