Subsets space a component of one of the mathematical ideas called Sets. A set is a collection of objects or elements, grouped in the curly braces, such together a,b,c,d. If a set A is a collection of also number and collection B consists of 2,4,6, then B is claimed to it is in a subset of A, denoted by B⊆A and A is the superset the B. Learn Sets Subset and Superset to recognize the difference.

You are watching: Difference between proper subset and subset

The facets of sets could be something such as a group of real numbers, variables, constants, totality numbers, etc. It consists of a null collection as well. Let us talk about subsets below with its types and examples.

Table that contents:

DefinitionProper SubsetImproper Subsets

What is a Subset in Maths?

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

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

Subset Symbol

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

Using this prize we can express subsets together follows:

A ⊆ B; which means Set A is a subset of set B.

Note: A subset have the right to be same to the set. That is, a subset have the right to contain all the aspects that are current in the set.

All Subsets that a Set

The subsets that any collection consists that all feasible sets including its elements and the null set. Let us know with the assist 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 that Subsets

Subsets room classified as

Proper SubsetImproper Subsets

A ideal subset is one that has a few elements that the original set whereas an not correct subset, consists of every aspect of the original collection along v the null 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

Improper Subset: 2,4,6

There is no specific formula to uncover the subsets, instead, we need to list lock all, to differentiate in between proper and improper one. The collection theory signs were developed by mathematicians to describe the collections of objects.

What are ideal Subsets?

Set A is considered to it is in a suitable subset of set B if set B includes at the very least one aspect that is not existing in set A.

Example: If collection A has facets as 12, 24 and collection B has elements as 12, 24, 36, then set A is the appropriate subset of B since 36 is not present in the collection A.

Proper Subset Symbol

A suitable subset is denoted through ⊂ and also is review as ‘is a appropriate subset of’. Using this symbol, we have the right to express a suitable subset for set A and collection B as;

A ⊂ B

Proper Subset Formula

If we have to pick n number of elements indigenous a set containing N number of elements, it have the right to be done in NCn number of ways.

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

How numerous subsets and proper subsets go a collection have?

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

Consider an example, If collection A has the elements, A = a, b, climate the proper subset of the provided subset room , a, and b.

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

We understand that the formula to calculate 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 improper Subset?

A subset which consists of all the facets of the original collection is called an wrong subset. That is denoted by ⊆.

For example: collection P =2,4,6 Then, the subsets of ns 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 suitable subsets and 2,4,6 is the improper subsets. Therefore, we have the right to write 2,4,6 ⊆ P.

Note: The empty set is an improper subset of itself (since it is equal to itself) yet it is a proper subset of any kind of other set.

Power Set

The power set is stated to be the repertoire of every the subsets. That is represented by P(A).

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

P(A) = ∅, a, b, a, b

To learn an ext in brief, click on the article link of strength set.

Properties that Subsets

Some that the essential properties that subsets are:

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

Also, read:

Subsets instance Problems

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

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

Solution: variety of elements in the collection = 10

Number of facets in the subset = 3

Therefore, the number of possible subsets comprise 3 elements = 10C3


Therefore, the variety of possible subsets containing 3 elements from the set S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is 120.

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

Solution: we can find a selection of examples of subsets in day-to-day life such as:

If we think about all the publications in a library together one set, then books pertaining to Maths is a subset.If every the items in a grocery store shop form a set, climate cereals form a subset.

See more: What Do You Call A 12 Sided Shape Called, What Is A 1000000000000000 Sided Shape Called

Example 3: find the number of subsets and the variety of proper subsets for the given collection A = 5, 6, 7, 8.