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 2ⁿ. 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 = 2³ = 2^number of elements of A. Thus, the formula to determine the number of subsets of a set with ‘n’ elements is 2ⁿ.

For example:

• If A has 2 members, it has 2² = 4 subsets.
• If A has 6 members, it has 2⁶ = 64 subsets.
• If A has 0 elements, it has 2⁰ = 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 2ⁿ where ‘n’ is the number of members in the set.