# What is Subset Mean in Math? | How to Find the Number of a Subset of a Set

If all members of **set** A are present in set B then we say that set A is a subset of set B. We also know that a set is a well-defined collection of distinct objects numbers, alphabets, or any items. If set A = {1,2,3} and set B = {1,2,3,4,5,6} we can say that set A is a subset of

Set B because all the members in set A are present in set B**.**

In this article learn about the subsets along with their **types of subsets** improper subsets and proper subsets explain with examples.

**What is a subset?**

If all members of set A are present in set B then we say that set A is a subset of set B. The set notation to denote a set A as a subset of set B is written as A ⊆ B.

There are two types of a subset

- Proper subset
- Improper subset

**For example:**

- A={1,3,5} is a subset of B={1,3,5,7,11}
- A=set of all odd numbers is a subset of B=set of the whole number
- Every set is a subset of itself and also the empty set (Φ) is also a subset of every set.

**Subset symbol**

There are two types of a subset of symbol

- ⊂, which is read as “is a subset of” but not equal to
- ⊆, which is read as “is a subset or equal to”

, we can write A ⊂ B (or) A ⊆ B. But there is a difference between these two symbols and the usage of each symbol depends upon the type of subset. There are two types of a subset

Proper subset and improper subset the symbol used for this is ⊂ is a proper subset the symbol used for this is ⊆ is an improper subset.

**How to find the number of a subset of a set**

The number of subsets of a set with n members is 2^{n}. For example, if A = {a, b, c}, then the number of members of A = 3. The subsets of A are { }, {a}, {b}, {c}, {a, b}, {a,c}, {b, c}, and {a, b, c}. So A has a total of 8 subsets and 8 = 2^{3} = 2^{number} of elements of A. Thus, the formula to determine the number of subsets of a set with ‘n’ elements is 2^{n}.

**For example:**

- If A has 2 members, it has 2
^{2}= 4 subsets. - If A has 6 members, it has 2
^{6}= 64 subsets. - If A has 0 elements, it has 2
^{0}= 1 subset (which is the empty set Φ)

**Summary**

- An empty set is always a subset of any given set.
- The set itself is a subset of its own.
- A proper subset can be a set with all elements except itself a set.
- The number of a set is 2
^{n}where ‘n’ is the number of members in the set.

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