Cardinality of Power Set
Cardinality (cardinality of a set means the number of elements of a set) of a power set denotes the number of elements present in the power set. It is denoted by |P(A)|. Thus, number of elements in the power set is given by:
|P(A)| = 2n
Where “n” is the number of elements of Set A.
Let’s consider an example for better understanding.
Example: Find the cardinality of the Power Set of A, where A = {1,2,9}.
Answer:
As |A| = 3, thus number of elements in Power Set of A = 2|A|
Thus, |P(A)| = 23 = 8
Therefore, there are 8 elements in the power set of A.
Power Set
Power Sets, also known as the “set of all subsets,” is one of the important concepts in Set Theory. Power Set is nothing but a collection of all the subsets of any set including the empty set, as the empty set is the subset of all possible sets. Power sets are used in various fields where a list of all possibilities from some finite number of elements is required, such as computer science, data analysis, and even artificial intelligence.
In this article, we will discuss all the topics related to Power Set in detail, including its definition, symbol, and examples. Other than that, we will also learn how to find power sets for any set and also see various solved examples for that. So, let us start our learning for the concept of Power Sets.
Table of Content
- What is Power Set?
- Power Set Example
- How to Find Power Set?
- Cardinality of Power Set
- Properties of Power Set