Equal and Equivalent set (Definition, Example, Symbol, Venn Diagram)

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}

Venn Diagram of Equal Sets
Venn diagram of unequal sets

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}

Venn diagram of equivalent sets

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)

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

Two sets are said to be equivalent if both the sets have the same number of elements.

Two sets are said to be equal if they have precisely the same elements whereas two sets are said to be equivalent if both the sets have an equal number of elements.

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

The difference of two equal sets in an empty set.

Let, A={1,2,3,4} & B={a,b,c,d}. The sets A and B are equivalent as the elements present in both the sets is the same. Cardinality n(A)=n(B)=4.

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