Find the Power Set n={1,2,3}

Problem

𝒫*({1,2,3})

Solution

1. Identify the elements of the given set n={1,2,3} The power set is the set of all possible subsets, including the empty set and the set itself.

2. List the subset with zero elements, which is the empty set ∅

3. List all subsets with exactly one element (singletons): {1} {2} and {3}

4. List all subsets with exactly two elements: {1,2} {1,3} and {2,3}

5. List the subset with all three elements: {1,2,3}

6. Combine all identified subsets into a single set. Since the original set has 3 elements, the power set must contain 2^3=8 elements.

Final Answer

𝒫*({1,2,3})={∅,{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

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