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What is power set?Obtain the power set p(s) if S(a,b,c)
The power set of a set, denoted as P(S), is the set of all possible subsets of the original set S. It includes the empty set, the original set, and all possible combinations of elements from the original set.
To find the power set of a set, you can use the following steps:
The cardinality (or size) of the power set P(S) of a set S is equal to 2^n, where n is the number of elements in the original set. This means that if a set S has n elements, its power set will have 2^n subsets.
Yes, the power set of a set can be empty if the original set is also empty. In this case, the power set will only contain the empty set and will have a cardinality of 1.
The power set of a set is always larger than the original set. This is because the power set includes all possible subsets, including the original set itself. However, the power set is not a proper superset of the original set, as it also includes the empty set as a subset.