# Subset, types, definitions, symbols, and examples

In mathematics, the subset is a section under sets. sets are collections of well-defined objects of the same kind. For example a collection of even numbers, or a collection of flowers. In this article, we will be discussing subsets, types, definitions symbols, and examples of subsets.

## What is a subset?

A subset is a set whose members are contained in another set. For example, if set A={2, 4, 6, 8,10,12} and set B={4, 8,12}. Then set B is a subset of set A. In the mathematic subset is denoted as . For example, if set Q ={ set of even numbers} and set P={2, 4, 6, 8}. Then P ⊂ Q. The symbol ⊂ means “subset of “. Note that the empty set is a subset of any given set.

## How to find a subset of a set.

In mathematics to find the subset of a given set, if the set has k number of elements, then the number of subsets of the given set is

2^n

Where n is the number of elements or members of the ser. For example, if set Q={a, b, c}. Set Q has three (3) members

\text{Therefore the number of a subset of set Q}=2^n, \text{where n=3}\\
\text{subset of Q}=2^3=8 \space\text{subsets. This means that set Q will have 8 subsets. Remember that an empty set ∅ is a subset of any set}\\


∴ the subsets of set Q = { }, {a}, {b}, {c}, {a,b},{a,c},{b,c},{a, b, c}.

## Types of subset

There are two main types of subsets.

• Proper subset

• Improper subset

## What is a proper subset?

The proper subset is a type of subset which contains at least one or more members of the original set but not all. In order words, a proper subset is a subset that contains some of the members of the original set. For example, if set A={1, 2, 3}. The proper subset of set A ={ }, {1},{2},{3},{1,2},{1,3},{2,3}. A proper subset is denoted as .

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## What is an improper subset?

The improper subset is a type of subset that contains all the members of the original set. For example, if set Q={1, 2, 3, 4}, the improper subset of set Q = {1, 2, 3, 4}. An improper subset is denoted as .

Practice the questions below on subsets

a) list all the proper and improper subsets of Q={1, 2, 3, 4}

b) List all the subsets of set A ={2, 3, 4, 5, 6}