175k views
5 votes
Does the power set incluide empty set

User Alrob
by
7.9k points

1 Answer

4 votes

Final answer:

Yes, the power set includes the empty set. The power set is the set of all subsets of a given set, which always contains the empty set as it is a subset of every set.

Step-by-step explanation:

The idea of a power set in mathematics refers to the set of all subsets of a given set, including both the original set itself and the empty set. To demonstrate this concept, let's consider a simple set, A = {1, 2}. The power set of A, denoted as P(A), includes the following subsets: the empty set (∅), the singleton sets {1} and {2}, and the entire set {1, 2}. Therefore, the power set of A is P(A) = {∅, {1}, {2}, {1, 2}}. As illustrated, the empty set is invariably a member of any power set because it is considered a subset of every set.

User Seb Kade
by
7.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories