Find the Power Set A=(5,6,7)

Problem

𝒫*(A)* where *A={5,6,7}

Solution

1. Identify the elements of the set A The set A contains 3 elements: 5 6 and 7

2. Determine the total number of subsets using the formula 2 where n is the number of elements. Since n=3 there are 2=8 subsets.

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

4. List all subsets containing exactly one element (singletons): {5} {6} and {7}

5. List all subsets containing exactly two elements: {5,6} {5,7} and {6,7}

6. List the set itself, which is the subset containing all three elements: {5,6,7}

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

Final Answer

𝒫*(A)={∅,{5},{6},{7},{5,6},{5,7},{6,7},{5,6,7}}

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