Find the Power Set A=(1,2,3,4)

Problem

𝒫*({1,2,3,4})

Solution

1. Identify the set A and its cardinality. The set is A={1,2,3,4} which contains n=4 elements.

2. Determine the number of elements in the power set. The power set 𝒫*(A) contains 2 elements, so 2=16 subsets.

3. List the subsets by size, starting with the empty set ∅

4. Find all subsets with 1 element: {1},{2},{3},{4}

5. Find all subsets with 2 elements: {1,2},{1,3},{1,4},{2,3},{2,4},{3,4}

6. Find all subsets with 3 elements: {1,2,3},{1,2,4},{1,3,4},{2,3,4}

7. Find the subset with 4 elements, which is the set A itself: {1,2,3,4}

8. Combine all found subsets into a single set.

Final Answer

𝒫*({1,2,3,4})={∅,{1},{2},{3},{4},{1,2},{1,3},{1,4},{2,3},{2,4},{3,4},{1,2,3},{1,2,4},{1,3,4},{2,3,4},{1,2,3,4}}

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