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## 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:

Serial No | Improper Subset | Proper Subset |

1 | For a set A to be an Improper Subset of B all the elements of A must be present in the set B. | For a set A to be a Proper 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. |

2 | For a set A to be an Improper Subset of set B, A and B may be equal sets. | For a set A to be a Proper Subset of B, A and B must not be equal. |

3 | A=\{1, 2, 3, 4\} B=\{1, 2, 3, 4\} A is an Improper Subset of B | A=\{1, 2, 3, 4\} B=\{1, 2, 3, 4\} A is not a Proper Subset of B |

4 | A=\{a, b, c, d, e\} B=\{a, b, c, d, e, f, g\} A is not an Improper Subset of B | A=\{a, b, c, d, e\} B=\{a, b, c, d, e, f, g\} A is also a Proper Subset of B |

## Frequently Asked Questions

### 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.

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I think you made a mistake in your table.

4.) It is meant to be A is not an improper subset of B

Yes, you are right. I have made the changes. Thank you..