Find the Power Set A=(2,3,4,5)

Problem

𝒫*({2,3,4,5})

Solution

1. Identify the set A={2,3,4,5} and its cardinality. Since there are 4 elements, the power set will contain 2=16 subsets.

2. List the empty set, which is a subset of every set: ∅

3. List all subsets containing exactly one element (singletons): {2} {3} {4} and {5}

4. List all subsets containing exactly two elements: {2,3} {2,4} {2,5} {3,4} {3,5} and {4,5}

5. List all subsets containing exactly three elements: {2,3,4} {2,3,5} {2,4,5} and {3,4,5}

6. List the set itself, which contains all four elements: {2,3,4,5}

7. Combine all identified subsets into a single set 𝒫*(A)

Final Answer

𝒫*({2,3,4,5})={∅,{2},{3},{4},{5},{2,3},{2,4},{2,5},{3,4},{3,5},{4,5},{2,3,4},{2,3,5},{2,4,5},{3,4,5},{2,3,4,5}}

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