Power Set of a Set
A set’s power set consists of every subset as well as the original set and the empty set. P(A) stands for the power set of a given set A. For example, If A = {1, 2}, then P(A) = {{ }, {1}, {2}, {1, 2}}. Here we can clearly see that all the subsets of A are contained in the P(A) i.e., power set of A.
Number of Subsets of a Set
For any set A, number of seusets are given using the following formula
Number of Subsets = 2n
Where n is number of elements in the set.
As power set contain all the subsets of any set, thus for a set A which has ‘n’ elements then P(A) has 2n elements.
Example: How many elements of power set can be formed if there are four elements in a set?
Answer:
Number of elements of power set with three elements are 24 = 16.
Subsets in Maths
Subsets in maths are a core concept in the study of Set Theory, similar to Sets. A group of elements, objects, or members enclosed in curly braces, such as {x, y, z} is called a Set, where each member of the set is unique. So for a set of {x, y, z} the possible subsets are {}, {x}, {y}, {z}, {x, y}, {y, z}, {z, x} or {x, y, z}. While defining a set its elements could be real numbers, constants, variables, or any other objects as well.
This article explores the concept of Subsets in detail and makes it easy to grasp for all the readers of the article without any regard to their academic level. All subtopics such as their meaning, definition, symbol, example, and many many more, are covered in the article with plenty of examples. So, let’s start our journey to the land of set theory and understand this concept of Subsets.
In this article, we have provided detailed information about what are subsets in maths, supersets in maths, proper subset, and improper subset with examples and FAQs.
Table of Content
- What are Subsets in Maths?
- Example of Subsets
- Power Set of a Set
- Types of Subsets
- Proper Subset
- Improper Subset
- Proper and Improper Subsets
- Subsets vs Supersets
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