Improper Subset
An improper subset contains includes both the null set and each member of the initial set. Improper subset can be equal to the original set. In improper subset the subset forming the original set is included. This is represented by the symbol ⊆.
Example: What will be the improper subset of set A = {1, 3, 5}?
Answer:
Improper subset: {}, {1}, {3}, {5}, {1,3}, {1,5}, {3,5} and {1,3,5}
Improper Subset Formula
For a collection of ‘n’ elements, the number of improper subsets is always 1. In other words, the number of improper subsets of a set is independent of the number of its elements.
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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