Find the Power Set s={2+x-3x^2-8x^3,1+x+x^2+5x^3}

Problem

𝒫*({2+x−3*x2−8*x3,1+x+x2+5*x3})

Solution

1. Identify the elements of the given set S The set contains two distinct polynomial elements: a=2+x−3*x2−8*x3 and b=1+x+x2+5*x3

2. Determine the number of elements in the power set. Since the cardinality of the set is n=2 the power set 𝒫*(S) must contain 2=2=4 subsets.

3. List all possible subsets of S These include the empty set, the subsets containing exactly one element (singleton sets), and the set itself.

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

Final Answer

𝒫*({2+x−3*x2−8*x3,1+x+x2+5*x3})={∅,{2+x−3*x2−8*x3},{1+x+x2+5*x3},{2+x−3*x2−8*x3,1+x+x2+5*x3}}

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