Subsets are a component of among the mathematical concepts called Sets. A collection is a collection of objects or elements, group in the curly braces, such as a,b,c,d. If a collection A is a repertoire of even number and set B is composed of 2,4,6, then B is claimed to be a subset the A, denoted through B⊆A and also A is the superset that B. Learn Sets Subset and Superset to know the difference.

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The elements of sets might be noþeles such as a team of genuine numbers, variables, constants, whole numbers, etc. It consists of a null collection as well. Let us talk about subsets below with its types and examples.

Table the contents:

DefinitionProper SubsetImproper Subsets

What is a Subset in Maths?

Set A is stated to be a subset of set B if every the facets of collection A are also present in set B. In various other words, set A is included inside set B.

Example: If set A has X, Y and collection B has actually X, Y, Z, then A is the subset the B because elements of A are likewise present in collection B.

Subset Symbol

In set theory, a subset is denoted by the symbol ⊆ and read as ‘is a subset of’.

Using this symbol we deserve to express subsets together follows:

A ⊆ B; which method Set A is a subset of collection B.

Note: A subset deserve to be same to the set. That is, a subset can contain all the elements that are present in the set.

All Subsets that a Set

The subsets the any collection consists the all possible sets including its elements and also the null set. Allow us understand with the help of an example.

Example: discover all the subsets of set A = 1,2,3,4

Solution: Given, A = 1,2,3,4

Subsets =

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


Types the Subsets

Subsets room classified as

Proper SubsetImproper Subsets

A appropriate subset is one that has a couple of elements that the original collection whereas an improper subset, consists of every facet of the original set along with the null set.

For example, if set A = 2, 4, 6, then,

Number the 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

Improper Subset: 2,4,6

There is no specific formula to find the subsets, instead, we need to list them all, to differentiate in between proper and improper one. The set theory icons were occurred by mathematicians to explain the collections of objects.

What are suitable Subsets?

Set A is considered to be a appropriate subset of set B if collection B includes at least one element that is not existing in set A.

Example: If set A has aspects as 12, 24 and set B has aspects as 12, 24, 36, then collection A is the suitable subset that B due to the fact that 36 is not current in the collection A.

Proper Subset Symbol

A appropriate subset is denoted through ⊂ and is check out as ‘is a proper subset of’. Utilizing this symbol, we deserve to express a proper subset for set A and set B as;

A ⊂ B

Proper Subset Formula

If we have to pick n variety of elements from a collection containing N number of elements, it can be done in NCn number that ways.

Therefore, the variety of possible subsets comprise n variety of elements indigenous a collection containing N number of elements is equal to NCn.

How numerous subsets and also proper subsets go a set have?

If a set has “n” elements, then the number of subset that the given set is 2n and also the number of proper subsets that the given subset is offered by 2n-1. 

Consider one example, If set A has the elements, A = a, b, climate the suitable subset that the given subset room , a, and b.

Here, the number of elements in the set is 2. 

We recognize that the formula to calculation the number of proper subsets is 2n – 1. 

= 22 – 1

= 4 – 1

= 3

Thus, the variety of proper subset because that the given set is 3 ( , a, b).

What is not correct Subset?

A subset which contains all the facets of the original collection is dubbed an improper subset. It is denoted by ⊆.

For example: set 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 space the proper subsets and 2,4,6 is the wrong subsets. Therefore, we have the right to write 2,4,6 ⊆ P.

Note: The empty set is one improper subset that itself (since the is same to itself) but it is a proper subset of any kind of other set.

Power Set

The power set is claimed to it is in the collection of all the subsets. It is represented by P(A).

If A is collection having facets a, b. Climate the power set of A will be;

P(A) = ∅, a, b, a, b

To learn more in brief, click the post link of strength set.

Properties that Subsets

Some that the important properties the subsets are:

Every collection is considered as a subset the the given collection itself. It method that X ⊂ X or Y ⊂ Y, etcWe deserve to say, one empty collection is thought about as a subset the every set. X is a subset that Y. It method that X is consisted of in YIf a set X is a subset of set Y, we can say that Y is a superset of X

Also, read:

Subsets example Problems

Example 1: How many variety of subsets comprise three elements can be developed from the set?

S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Solution: variety of elements in the set = 10

Number of facets in the subset = 3

Therefore, the variety of possible subsets containing 3 aspects = 10C3


Therefore, the variety of possible subsets comprise 3 facets from the collection S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is 120.

Example 2: Given any two real-life instances on the subset.

Solution: we can find a selection of instances of subsets in daily life such as:

If we consider all the books in a library as one set, then books pertaining come Maths is a subset.If all the items in a grocery shop form a set, climate cereals form a subset.

Example 3: discover the number of subsets and also the variety of proper subsets because that the given collection A = 5, 6, 7, 8.

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Given: A = 5, 6, 7, 8

The number of elements in the set is 4

We know that,

The formula to calculation the number of subsets that a given collection is 2n

= 24 = 16

Number the subsets is 16

The formula to calculation the number of proper subsets that a given collection is 2n – 1

= 24 – 1

= 16 – 1 = 15

The variety of proper subsets is 15.

In collection theory, a set X is identified as a subset the the other set Y, if all the elements of set X must be present in the set Y. This have the right to be symbolically stood for by X ⊂ Y