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:

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

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