## What is equal set?

Two sets are said to be **Equal Sets** if and only if all the elements present in both sets are precisely the same.

## Symbol of equal sets

If two sets, say A and B are equal, then mathematically, it can be written as:

A=B

## Equal Sets Examples

## Which of the following are equal sets?

A = {a, b, c, d}

B = {b, c, a, d}

C = {a, b, c, 2}

Here, set A and set B are **Equal Sets** because both the sets have **precisely the same elements** even if the order of the elements is not the same. If we rearrange the elements in set B, then it will be the same as set A.

Set A and set C are not equal because the 4th element in set A is 'd’ and in set C is ‘2’ which are not the same.

Similarly, set B and set C are not **Equal Sets**.

## What is Equivalent Set?

Two sets are said to be **Equivalent Sets** if the sets have exactly the same **number of elements** even if the **elements are not the same.** Therefore, two **Equivalent Sets** have the same cardinality.

## Symbol of Equivalent sets

The symbol for representing **Equivalent Sets **is \leftrightarrow . If the two sets A and B are **Equivalent Sets**, then

A\leftrightarrow B

## Example of Equivalent sets

Let us consider two sets A and B as,

A = {1, 2, 3, 4}

B = {a, b, c, d}

In the above two sets A and B, the elements of set A are {1, 2, 3, 4} and the elements of set B are {a, b, c, d}, which are not equal. However, the number of elements present in both sets are 4. Therefore, the above sets are said to be **Equivalent Sets** even if the elements are not the same.

Cardinality of the above sets are

n(A)=n(B)=4

## Frequently Asked Questions (FAQ)

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- Definition and Example of Finite Sets
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- Infinite Sets
- Singleton Set

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