what is subset?

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gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

Subset means part of something bigger which contain similar items. Subset is a commonly used term in Set Theory in Mathematics.

A given set A is called a "subset" of another set B, if all elements of A are also the elements of B. 

For example, let set A = {0,1,2,3} and B = {0,1,2,3,4,5},

then set A is a subset of set B, since all the elements of A (namely, 0,1,2 and 3) are also the elements of set B.

Mathematically, it can be denoted as:

A I B   or, `A sube B`

Hope this helps.

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Nolan McShea | Student, Grade 11 | (Level 2) Honors

Posted on

subset is a part of a set (you can see what a set is here). For example, if our set is {1,2,3,4,5}, a subset of that will be {1,2,3}. Another subset can be {1,2}, or {3,4}, or {1}. However, {2,12} is not a subset because the 12 is NOT included in the original set.

There are also proper subsets, which are more obvious than you think. It's kind of hard to explain, so let me give you an example:

{1,2,3,4,5} is the original set.

{1,2,3,4,5} is a subset, but it is NOT a proper subset.

{1,2,3,4}, however, is a proper subset.

The subset of the original set must have values only from the original set, and there is at least one value in the original set that is not included in that subset in order for that subset to be a proper subset.

One last thing: an empty set (or a set with nothing in it) can be considered a subset of an original set, because it follows the rules of a subset! Weird, huh?

Hope I helped!

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kspcr111's profile picture

kspcr111 | In Training Educator

Posted on

In mathematics, the set A is a subset of a set B, if all the elements in the set A are contained in set B then all the elements of A are also present in set B .But it dosn't mean that all elements of set B are in set A. The other names for the subset are also  called as inclusion or containment.

Let us see some examples :

1) 

Let set A and set B be two set containing  elements . In the Figure 1,

it clearly states that set A is subset of set B , as all the elements of set A are also the elements of set B

2) 

Let set A , set B  and set C be the sets containing  elements . In the Figure 2,

it clearly has 3 subsets

-> set A is subset of set B

-> set B is subset of set C

-> set A is subset of set C

So, this is the concept of subset in set theory. Hope this will help you to understand better.  :)

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kspcr111 | In Training Educator

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sorry , i forgot to upload the images , so i am doing in this 

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