Find the Power Set s={1,3,5,7}

Problem

𝒫*({1,3,5,7})

Solution

1. Identify the number of elements in the set S={1,3,5,7} Since there are n=4 elements, the power set will contain 2=2=16 subsets.

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

3. List all subsets containing exactly one element (singletons): {1} {3} {5} and {7}

4. List all subsets containing exactly two elements: {1,3} {1,5} {1,7} {3,5} {3,7} and {5,7}

5. List all subsets containing exactly three elements: {1,3,5} {1,3,7} {1,5,7} and {3,5,7}

6. List the set itself, which is the only subset containing four elements: {1,3,5,7}

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

Final Answer

𝒫*({1,3,5,7})={∅,{1},{3},{5},{7},{1,3},{1,5},{1,7},{3,5},{3,7},{5,7},{1,3,5},{1,3,7},{1,5,7},{3,5,7},{1,3,5,7}}

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