What is the main purpose of a power set?

The main purpose of a power set is to list all combinations of elements from the original set, which is precisely what option B highlights. A power set is defined as the set of all subsets of a given set, including the empty set and the set itself. Therefore, if you have a set with n elements, the power set will contain 2^n subsets, encompassing every possible arrangement of those elements. This includes individual elements, pairs, triples, and so on, ultimately exploring all possible combinations.

For example, if we take a set with elements {a, b}, the power set would include the subsets: {}, {a}, {b}, and {a, b}. This clearly demonstrates how the power set captures every possible combination of elements available in the original set. Understanding the power set is crucial in set theory, as it forms the basis for further mathematical concepts, such as functions, relations, and more complex operations involving sets.