A **relationship** is a **link** or one **correspondence** . In the case of **mathematical relationship** , It's about the **correspondence that exists between two sets** : Each element of the first set corresponds to at least one element of the second set.

When each element of a set corresponds only to each other, we talk about **function** . This means that mathematical functions are always, in turn, mathematical relations, but that relations are not always functions.

In a mathematical relationship, the first set is known as **domain** , while the second set is called **rank** or **travel** . The mathematical relationships between them can be plotted in the scheme called **Cartesian plane** .

Suppose the **domain** is called **M** and the range, **N** . A mathematical relationship of **M** in **N** it will be a subset of the cartesian product **M x N** . Relationships, in other words, will be ordered pairs that link elements of **M** with elements of **N** .

Yes **M = {5, 7} and N = {3, 6, 8}** , the Cartesian product of **M x N** they will be the following ordered pairs:

*M x N = {(5, 3), (5, 6), (5, 8), (7, 3), (7, 6), (7, 8)}*

With this **product** Cartesian, different relationships can be defined. The mathematical relationship of the set of pairs whose second element is less than **7** is *R = {(5, 3), (5, 6), (7, 3), (7, 6)}*

Another mathematical relationship that can be defined is that of the set of pairs whose second element is **pair** : *R = {(5, 6), (5, 8), (7, 6), (7, 8)}*

The **Applications** of mathematical relationships transcend the limits of science, since in our daily life we usually make use of its principles, often unconsciously. *Humans, buildings, appliances, movies and friends*, among many others, are some of the *sets* most common of interest to our species, and we establish relationships with each other every day to organize and participate in our activities.

According to the number of sets that participate in the Cartesian product, it is possible to recognize various types of mathematical relationship, some of which are briefly defined below.

**Unary relationship**

A unary relationship occurs when a single set is observed, and it can be defined as the subset of the elements that belong to it and meet a **condition** determined, expressed in the relationship. For example, within the set of natural numbers, we can define a unary relationship (which we will call **P** ) of the even numbers, so that of all the elements of this set, we will take those that respond to this condition and form a subset, which begins as follows: *P = {2,4,6,8,…}*

**Binary relationship**

As the name implies, this mathematical relationship starts from two sets, and therefore the complexity increases considerably. The elements of both can be related in more ways, and the resulting subsets are expressed as ordered pairs, as demonstrated in previous paragraphs. In mathematics, this is usually in the background in many of the most common functions, which have as variables **and** and **x** , since a pair of values (one of each axis) that allow solving a **equation** (that meet the condition).

**Ternary Relationship**

When we define a condition that elements from three different sets must meet, we talk about a ternary relationship, and the result is one or more **terna** (the equivalent to the ordered pairs but with three elements). Returning to the set of natural numbers, which allows us to make simple calculations, an example of a mathematical relationship of this type is one in which *a - b = c*, so we could get a subset that starts like this: *R = {(3,2,1), (4,3,1), (5,3,2),…}*