# Improper Subset (Definition, Symbol, Example, Venn Diagram)

## Definition of Improper Subset

A set $A$ is called Improper Subset of set $B$ only when all the elements of set $A$ and $B$ are equal to each other and there is no extra element in any of the sets. Improper Subsets can simply be called Subsets. If a set is an Improper Subset of another set, then both sets are equal and have the same Cardinality.

## Improper Subset Symbol

The Improper Subset Symbol is similar to the symbol of the subset. If set $A$ is an Improper Subset of $B$ then mathematically it can be written as,

$\displaystyle A\subseteq B$

## Example of Improper Subset

To understand the fundamentals of Improper Subset, let us consider two sets $A$ and $B$ as given below.

$A$ = {1, 2, 3}

$B$ = {1, 2, 3}

The above figure shows the Improper Subset Venn Diagram. From the figure, it is clear that all the elements of set $A$ are present in the set $B$ and both the sets are equal. There is no extra element in any of the given sets. Therefore, $A$ is called the Improper Subset of $B$ and vice versa. Also, $A$ and $B$ are called equal sets.

## Difference between Improper Subset and Proper Subset | Proper subset vs Improper subset

The Differences between Improper Subset and Proper Subset are as follows:

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