Find the Power Set A=(1,2,3,4,5,6)

Problem

𝒫*({1,2,3,4,5,6})

Solution

1. Identify the set A and its cardinality. The set is A={1,2,3,4,5,6} which contains n=6 elements.

2. Determine the number of elements in the power set. The power set 𝒫*(A) contains 2 elements, so 2=64 subsets.

3. List all subsets by grouping them by size, starting from the empty set ∅ and ending with the set A itself.

4. Construct the power set by collecting all 64 subsets into a single set.

Final Answer

𝒫*({1,2,3,4,5,6})={∅,{1},{2},{3},{4},{5},{6},{1,2},{1,3},{1,4},{1,5},{1,6},{2,3},{2,4},{2,5},{2,6},{3,4},{3,5},{3,6},{4,5},{4,6},{5,6},{1,2,3},{1,2,4},{1,2,5},{1,2,6},{1,3,4},{1,3,5},{1,3,6},{1,4,5},{1,4,6},{1,5,6},{2,3,4},{2,3,5},{2,3,6},{2,4,5},{2,4,6},{2,5,6},{3,4,5},{3,4,6},{3,5,6},{4,5,6},{1,2,3,4},{1,2,3,5},{1,2,3,6},{1,2,4,5},{1,2,4,6},{1,2,5,6},{1,3,4,5},{1,3,4,6},{1,3,5,6},{1,4,5,6},{2,3,4,5},{2,3,4,6},{2,3,5,6},{2,4,5,6},{3,4,5,6},{1,2,3,4,5},{1,2,3,4,6},{1,2,3,5,6},{1,2,4,5,6},{1,3,4,5,6},{2,3,4,5,6},{1,2,3,4,5,6}}

Want more problems? Check here!