Hello, welcome to lesson three. After completing this lesson, you should understand what a relation is know the definition of a relation and be able to represent a relation in three different ways as a set of ordered pairs as a table of values and as an arrow diagram. So, what is a relation? Most of us know what a non mathematical relation is, for instance, father, mother, brother, sister, uncle, cousin, nephew. These are all examples of everyday relations. Now, let me introduce you to the three children in the math family.

There's Henry Ingrid, and James. There are two brothers and a sister. We could describe their relationship with each other as is a sibling of we say that Henry is a sibling of Ingrid. We also say that Ingrid is a sibling of James and that James is a sibling of Henry. Now we could write this relation in the form of ordered pairs like this. Henry is a sibling of Ingrid is written as the ordered pair, Henry, Ingrid like this.

Similarly, we can write Ingrid is a sibling of James as the ordered pair, Ingrid James, like this and j As a sibling of Henry, as this ordered pair, James Henry like this. However, we also know that if Henry is a sibling of Ingrid, then Ingrid is a sibling of Henry. And similarly, if Ingrid is a sibling of James, then James is a sibling of Ingrid. And also, if James is a sibling of Henry, then Henry is a sibling of James. So the complete set of ordered pairs for the relation is a sibling looks like this. With Henry and Ingrid, Henry, James, Ingrid, Henry, Ingrid, James, James, Ingrid, James Henry.

But there are other ways of writing this information. We can write the information in a table like this. The relation is is a symbol off, and the values of sibling one and sibling two are linked in pairs, as you can see in the table. Now a third way to represent the relation is by using what we call an arrow diagram. we list the names Henry, Ingrid and James like this. Write down the relation is a sibling of, and then write down the names again like this.

And we use arrows to show the relations between the three children, Henry and Ingrid, Henry and James, Ingrid and Henry, Ingrid and James, James and Henry, James and Ingrid. Now, we use mathematics to model the world around us. We can describe the relationship between two different measurable quantities accurately using mathematics. We often use an equation for This, like y equals x squared. For example, let's look at the relation y equals x squared. We'll start by making a table of values.

And we'll use these values for x, negative three, negative two, negative 1012, and three. Using the equation, we can calculate the corresponding values of y for these particular values of x. When x equals negative three, y equals nine. When x equals negative two, y equals four, when x equals negative one, y equals one, when x equals zero, y equals zero. When x equals one, y equals one, when x equals two, y equals four, and when x equals three, y equals nine We can use this table of values to write down the set of ordered pairs like this, negative three and nine, negative two and four, negative one and one, zero and 01 and one, two and four, and three and nine. And here they are together, the table of values and the set of ordered pairs.

Now we can use either the table of values, or the set of ordered pairs. To draw the corresponding arrow diagram. list the x values like this. Now list the y values. write down the equation y equals x squared, showing the relationship and use arrows to link the related pairs of values. Negative three and nine, negative two and four Negative one and one, zero and 01 and one, two, and four, and three and nine.

Now we've used three different ways to show a relation. The most common way is probably using a set of ordered pairs. More formally, we say that a relation is a rule, by means of which each element of a first set is associated with at least one element of a second set. Let's summarize what you've learned in this lesson. A relation refers to the way a number of things are connected. We can show a relation using a set of ordered pairs, or by a table of values, or by an arrow diagram.

Our definition of a relation is a relation is a rule by means of which each element of a first set is associated with connected to at least one element of a second set.