A relation is a relationship between two sets of elements. An example is a list matching students to their heights. A relation can also describe a function, such as an input number being added to 3 to produce the output. The domain is the set of all possible inputs, and the range is the set of all possible outputs. A relation maps elements of the domain to elements of the range. There are four types of relations: one-to-one, one-to-many, many-to-one, and many-to-many, depending on whether elements of the domain and range are unique or can have multiple mappings.

1. 7.1 – EXPLAIN CONCEPTS ASSOCIATED WITH RELATIONS
Objective: At the end of this lesson you will be able to explain basic concepts associated with
relations.
First, we need to know what a relation is.
A relation is simply a relationship between two sets of elements.
An example of a relation is a list of students in a class matched to their heights.
Student Heights (feet)
Matthew 5’10
Marc 6’2
Luke 5’11
Let us look at another example. Say we had a device. When we put numbers into this device,
the machine adds 3 to the number and the answer is displayed.. If 2 is the input, 5 is the output
(2 + 3 = 5).
We would call this relation:
Y = x + 3
where x is the input ( number entered )
y is the output
All the numbers that are entered ( entrada ) ( x ) are members of something called the domain.
In this example, the domain is all real numbers.
The numbers that outputted ( imprimir ) ( y) are are members of something called the range.
In mathematical terms, using the same example with 2, if 2 is entered and 5 is outputted, we
say that 2 maps onto 5, or that 5 is the image of 2.

2. 7.1 – EXPLAIN CONCEPTS ASSOCIATED WITH RELATIONS
Since all the numbers entered are real numbers, and 3 is added to each of these, then the
output must be a real-number, right? Well, all the possible or allowed outputs of the relation
are called the codomain.
You also need to be aware of the types of relations. There are 4 types of relations:
1) One to One – every member of the domain maps to a unique member of the range
2) One to many – members of the domain map to more than one member of the range
3) Many to One – many members of the domain map onto the same member of the range
4) Many to Many – many members of the domain map onto many members of the range
In the next section you will learn how to represent these relations.