Obtain the power set p(s) if S(a,b,c)

Thread starter judex
Start date Oct 7, 2008
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Power Power set Set

In summary, the power set of a set, denoted as P(S), is the set of all possible subsets of the original set S. To find the power set, one can list out all elements, write down all possible combinations, remove duplicates, and arrange in ascending order. The cardinality of the power set is 2^n, where n is the number of elements in the original set. It can be empty if the original set is empty. The power set is always larger than the original set, but not a proper superset as it includes the empty set.

Oct 7, 2008

judex

What is power set?Obtain the power set p(s) if S(a,b,c)

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Oct 7, 2008

statdad

Homework Helper

If [tex] \mathcal{A} [/tex] is a set, its power-set is the collection of its subsets (empty, non-empty, proper, non-proper, all of them)

Related to Obtain the power set p(s) if S(a,b,c)

1. What is the power set of a set?

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.

2. How do you find the power set of a set?

To find the power set of a set, you can use the following steps:

List out all the elements of the set.
Write down all possible combinations of these elements, including the empty set.
Remove any duplicate subsets.
Arrange the subsets in ascending order based on the number of elements they contain.

3. What is the cardinality of the power set of a set?

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.

4. Can the power set of a set be empty?

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.

5. What is the relationship between a set and its power set?

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.