Find the Power Set k(x,y,z)=(k^2x,k^2y,k^2z)

Problem

𝒫*({x,y,z})

Solution

1. Identify the set for which the power set is being found. Based on the input, the set is S={x,y,z}

2. Determine the number of elements in the power set. Since the set S has n=3 elements, the power set 𝒫*(S) will have 2=2=8 elements.

3. List all possible subsets of S starting with the empty set and moving through subsets of size 1, 2, and 3.

4. Construct the power set by grouping all identified subsets into a single set.

Final Answer

𝒫*({x,y,z})={∅,{x},{y},{z},{x,y},{x,z},{y,z},{x,y,z}}

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