How To Find Number Of Subsets
Subset is part of one of the mathematical concepts called Sets. A set is a collection of objects or elements, grouped in curly braces, such as {a, b, c, d}. If a set A is the set of even numbers and the set B consists of {2,4,6}, then B is said to be a subset of A, denoted FIRE, and A is a subset of B Learn Subset And Superset to understand the difference. The elements of the set can be anything such as a group of real numbers, variables, constants, integers, etc. It also includes an empty set. Let us discuss the subset here with its types and examples.Table of contents:
- Definition
- Types
- Set of real numbers
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- The appropriate subset notation
- Formula
- Subsets and Appropriate Subsets
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- Subset does not match
- Characteristic
- Solved examples
- Frequently asked questions
What is a subset in Mathematics?
Contents
Set A is said to be a subset of set B if all the elements of set A are also in set B. In other words, set A is contained within set B. Example: If set A is contained within set B, for example A has {X, Y} and set B has {X, Y, Z} then A is a subset of B because the elements of A are also in set B.
Subset icons
In set theory, a subset is denoted by the symbol ⊆ and is read as ‘is a subset of’. Using this notation, we can represent the subsets as follows: A ⊆ B; means that Set A is a subset of Set B. Note: A subset can be equal to that set. That is, a subset can contain all the elements contained in that set.
All subsets of a set
The subsets of any set include all possible sets including its elements and the empty set. Let us understand with the help of an example. Example: Find all subsets of set A = {1,2,3,4} Solution: Given, A = {1,2,3,4} Subset = {} {1 }, {2} , {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,2, 3}, {2,3,4}, {1,3,4}, {1,2,4} {1,2,3,4}
Types of subsets
The subsets are classified as
- Set of real numbers
- Subset does not match
The appropriate subset is the one that contains some elements of the original set while the unsuitable subset contains all the elements of the original set along with the empty set. For example, if set A = {2, 4, 6} then Number of subsets: {2}, {4}, {6}, {2,4}, {4,6}, {2, 6}, {2,4,6} and Φ or {} .Proper Subsets: { }, {2}, {4}, {6}, {2,4}, {4,6}, {2,6 } Inappropriate subset: {2,4,6} Read more: how to restart pokemon ultra moonThere is no specific recipe to find subsets, we have to list them all instead them to distinguish between subsets and nonconforming sets. Set theory notation was developed by mathematicians to describe sets of objects.
What is the appropriate subset?
Set A is considered to be an appropriate subset of Set B if Set B contains at least one element that is not present in Set A. Example: If Set A has elements of {12, 24} and set B has elements {12, 24, 36} then set A is a suitable subset of B because 36 is not in set A.
The appropriate subset notation
A suitable subset is denoted ⊂ and read as ‘is a suitable subset of’. Using this notation, we can express a suitable subset for set A and set B as; A B
Proper Subset Formula
If we have to choose n number of elements from a set containing N number of elements then it can be done in number of ways NCn So the number of possible subsets containing n number of elements from a set containing N number elements are equal to NCn.
How many subsets and appropriate subsets does a set have?
If a set has “n” elements, then the number of subsets of the given set is 2n and the number of appropriate subsets of the given subset is 2n-1. Consider an example, If the set A has elements, A = {a, b}, then the appropriate subset of the given subset is {}, {a} and {b}. Here, the number of elements in the set is 2 We know that the formula for the number of subsets is 2n – 1. = 22 – 1 = 4 – 1 = 3 Therefore, the appropriate number of subsets of the given set is 3 ({}, {a}, {b}).
What is a non-conforming subset?
A subset containing all the elements of the original set is called a non-conforming subset. It is denoted by ⊆.For example: Let P = {2,4,6} Then the subsets of P are; {}, {2}, {4}, {6}, {2,4}, {4,6}, {2,6} and {2,4,6}. Where, {}, {2}, {4}, {6}, {2,4}, {4,6}, {2,6} are the appropriate subsets and {2 , 4,6} are subsets do not match. Therefore, we can write {2,4,6} ⊆ P.Note: The drum set Is one its own mismatched subset (because it is equal to itself) but it is an appropriate subset of any other set.
The source
The the source is said to be the set of all subsets. It is represented by P(A). If A is a set with elements {a, b}. Then the set of powers of A will be; P(A) = {∅, {a}, {b}, {a, b}} To learn more briefly, click on the article link on power sets.
Attribute of subset
Read more: how to reheat olive garden bread | Top Q&A Some important properties of a subset are:
- Every set is considered to be a subset of the given set itself. Means X ⊂ X or Y ⊂ Y, etc
- It can be said that an empty set is considered as a subset of all sets.
- X is a subset of Y. That means X is contained in Y
- If the set X is a subset of the set Y, we can say that Y is a subset of X .
Also, read:
- Set for Grade 11
- Set subsets and subsets
- Union of Ministries
- Universal set
Subset example problem
Example 1: How many three-element subsets can be formed from that set?S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}Solution: Number of elements in a set = 10Number of elements in a subset = 3 Therefore, the number of subsets that can contain 3 elements = 10C3Therefore, the number of possible subsets containing 3 elements from the set S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is 120. Example 2: Give any two real-life examples on the subset.Solution: We can find many examples of subsets in daily life like:
Example 3: Find the number of subsets and the number of appropriate subsets of the given set A = {5, 6, 7, 8}.Solution:Given: A = {5, 6, 7, 8} The number of elements of the set is 4We know that, The formula for the number of subsets of the given set is 2n = 24 = 16The number of subsets is 16The formula for the number of sets is the appropriate subset of a given set is 2n – 1 = 24 – 1 = 16 – 1 = 15 The number of suitable subsets is 15. Learn more about set theory notation and other related topics. Sign up with BYJU’S – Learning app today.Read more: How to find nudity on tik tok
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