Find the Power Set s={4,8,12,16,20}

Problem

𝒫*({4,8,12,16,20})

Solution

1. Identify the number of elements in the set S={4,8,12,16,20} Since there are n=5 elements, the power set will contain 2=2=32 subsets.

2. List the empty set and the set itself, which are always members of the power set. These are ∅ and {4,8,12,16,20}

3. Determine all subsets containing exactly one element (singletons): {4} {8} {12} {16} and {20}

4. Determine all subsets containing exactly two elements: {4,8} {4,12} {4,16} {4,20} {8,12} {8,16} {8,20} {12,16} {12,20} and {16,20}

5. Determine all subsets containing exactly three elements: {4,8,12} {4,8,16} {4,8,20} {4,12,16} {4,12,20} {4,16,20} {8,12,16} {8,12,20} {8,16,20} and {12,16,20}

6. Determine all subsets containing exactly four elements: {4,8,12,16} {4,8,12,20} {4,8,16,20} {4,12,16,20} and {8,12,16,20}

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

Final Answer

𝒫*({4,8,12,16,20})={∅,{4},{8},{12},{16},{20},{4,8},{4,12},{4,16},{4,20},{8,12},{8,16},{8,20},{12,16},{12,20},{16,20},{4,8,12},{4,8,16},{4,8,20},{4,12,16},{4,12,20},{4,16,20},{8,12,16},{8,12,20},{8,16,20},{12,16,20},{4,8,12,16},{4,8,12,20},{4,8,16,20},{4,12,16,20},{8,12,16,20},{4,8,12,16,20}}

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