Find the Power Set Y=(3,6,8)

Problem

𝒫*({3,6,8})

Solution

1. Identify the elements of the set Y={3,6,8} The set contains n=3 elements.

2. Determine the total number of subsets using the formula 2 Since 2=8 the power set will contain 8 elements.

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

4. List all subsets containing exactly one element (singletons): {3} {6} and {8}

5. List all subsets containing exactly two elements: {3,6} {3,8} and {6,8}

6. List the set itself, as every set is a subset of itself: {3,6,8}

7. Combine all identified subsets into a single set to form the power set 𝒫*(Y)

Final Answer

𝒫*({3,6,8})={∅,{3},{6},{8},{3,6},{3,8},{6,8},{3,6,8}}

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