Representing Relations

Learn multiple ways to represent relations using tables, graphs, and equations. Math 10-C.

Lesson 7.1 of Relations and Functions in Math 10C — Alberta curriculum lessons.

What you'll learn in this lesson

• Sets, Elements, and Relations. Learn what a set and a relation are, and discover the key rule that order does not matter when listing a set.
• Four Ways to Show a Relation. Explore tables, arrow diagrams, ordered pairs, and graphs as four equivalent styles for displaying the same relation.
• Working with Numeric Relations. Practice sorting number sets by even and odd, prime and composite, and rational and irrational categories.

Inside the lesson — a free preview

What Is a Set?

Definition — Set. A set is a collection of distinct objects grouped together because they have something in common.

We write a set inside braces \ \.

Example: \-2, -1, 0, 1, 2\

Key Rule — Order Does Not Matter. When we list a set, the order of the elements does not change the set.

The set \-2, -1, 0, 1, 2\ is exactly the same set as \2, 0, -2, 1, -1\.

Think of a bag of groceries — whether the milk goes in before or after the bread, it is still the same bag of groceries.

A set only cares about what is inside it, not the arrangement.

What Is a Relation?

Definition — Relation. A relation connects the elements of one set to the elements of another set using some rule or relationship.

A relation is just a rule that pairs things up. You already understand relations from everyday life: "is the parent of", "is the capital of", "costs". Math just makes the pairing precise.

Example — Food Groups. Set 1: \Cheese, Apples, Carrots, Lettuce, Milk, Yogurt, Bananas, Tomatoes, Broccoli, Butter, Ice Cream, Potatoes\

Set 2: \Dairy, Produce\

The relation here is "belongs to the food group". Cheese relates to Dairy. Apples relate to Produce. Every item in Set 1 gets connected to a category in Set 2.

Overview of the Four Styles

The Four Representation Styles. The same relation can be displayed in several ways. The four main styles are:

1. Tables

2. Arrow Diagrams

3. Ordered Pairs

4. Graphs (numbers only)

Note: Graphing only works when both sets are numbers. For relations involving words (like foods and food groups), we use the first three styles.

Worked example: Even and Odd

Sorting \-2, -1, 0, 1, 2, 3, 4, 5\ into Even and Odd. A number is even if it divides evenly by 2, and odd if it does not.

Important: Zero is even, since 0 ÷ 2 = 0 with no remainder.

Negative numbers follow the same rule: -2 ÷ 2 = -1 with no remainder, so -2 is even.

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