Find the Power Set {1/8,1/16,1/24,1/32}

Problem

𝒫*({1/8,1/16,1/24,1/32})

Solution

1. Identify the elements of the given set S={1/8,1/16,1/24,1/32} The set contains n=4 elements.

2. Determine the number of subsets in the power set using the formula 2 Since n=4 there are 2=16 subsets.

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

4. Find all subsets with 1 element: {1/8} {1/16} {1/24} {1/32}

5. Find all subsets with 2 elements: {1/8,1/16} {1/8,1/24} {1/8,1/32} {1/16,1/24} {1/16,1/32} {1/24,1/32}

6. Find all subsets with 3 elements: {1/8,1/16,1/24} {1/8,1/16,1/32} {1/8,1/24,1/32} {1/16,1/24,1/32}

7. Find the subset with 4 elements, which is the set itself: {1/8,1/16,1/24,1/32}

Final Answer

𝒫*({1/8,1/16,1/24,1/32})={∅,{1/8},{1/16},{1/24},{1/32},{1/8,1/16},{1/8,1/24},{1/8,1/32},{1/16,1/24},{1/16,1/32},{1/24,1/32},{1/8,1/16,1/24},{1/8,1/16,1/32},{1/8,1/24,1/32},{1/16,1/24,1/32},{1/8,1/16,1/24,1/32}}

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