Equal And Equivalent Sets: 2 Examples And 5 Differences

In mathematics, there are various sorts of sets, each of which is unique. Some pupils might require assistance understanding what equal and equivalent sets are. I’ve chosen to write this essay to throw some light on this type of set as a result.

As you are aware, a set is an illustration of a collection of components shown in curly brackets. Additionally, a capital letter is used to denote a set. For instance, B = 2, 3, 4, and 5. The set B in this situation consists of the elements 2, 3, 4, and 5. B is a set, as indicated by the curved brackets.

Equivalent Sets

A set is a collection of elements, as I mentioned previously. These components are what will enable us to understand what comparable sets are.

Two sets must have the same cardinality (number of elements) in order for them to be equivalent.

n(A) = n(B)

For example,

A = {2, 3, 7, 9, 10, 12, 15}

B = {12, 23, 24, 34, 55, 56, 31}

Set A of the example above has seven components, and set B also has seven. Thus, if you add up the numbers in the two sets, you get seven (7).

Set A is equivalent to set B, one could say. In mathematics, it can be expressed as follows:

A ~ B since n(A) = n(B)

Equal Sets

The cardinality and elements must match exactly for two sets to be equal; the elements’ order is irrelevant.

Example: A = {5, 6, 9, 10} and B = {10, 6, 9, 5}

The elements in sets A and B are the same, but their arrangements are different. Since the exactness of the elements, rather than the order of the elements, determines whether a set is equal.

As a result, A = B.

Differences Equal and Equivalent Sets