Find the Power Set (7,7)

Problem

𝒫*({7,7})

Solution

1. Simplify the set by removing duplicate elements. In set theory, the set {7,7} is equivalent to the singleton set {7}

2. Identify the definition of a power set. The power set 𝒫*(S) is the set of all possible subsets of S including the empty set ∅ and the set S itself.

3. List all subsets of the simplified set {7} The subsets are the empty set ∅ and the set containing the single element {7}

4. Construct the power set by grouping these subsets into a new set.

Final Answer

𝒫*({7,7})={∅,{7}}

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