# 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:

### What is an Improper Subset with example?

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.

For Example,

A={a, b, c, d}

B={a, b, c, d}

All the elements of set A present in set B. Therefore, A is an Improper Subset of set B or vice versa and it can be written as,

A ⊆ B

B ⊆ A

### What is the difference between subset and proper subset?

The difference between Subset and Improper subset is:
Subset: For a set, A to be a Subset of B all the elements of set A must be present in set B and set B must contain at least one extra element which is not present in A.
Improper Subset: For a set, A to be an Improper Subset of B all the elements of A must be present in the set B.

### Is phi an improper subset?

The empty set phi is an improper subset of itself only. For any other sets, Phi is a Proper Subset.

### What is the difference between Improper Subset and Equal set?

There is no difference between the Improper subset and Equal set. For a set A to be an Improper subset of another set B, all the elements of set A must be present in set B and there must not be any extra element in the set B. Therefore, it can be concluded that the Improper Subset and Equal set are similar.