Presentation of relation using Arrow diagram

Presentation of Relation Using Arrow Diagram

A relation is a set of ordered pairs that connects elements from one set to another. There are several ways to represent a relation: tabular form, roster form, arrow diagram, and by identifying its domain and range.

1. Representation in Tabular Form

The tabular form displays the relation as a table where each row represents a pair from the relation.

| Input (x) | Output (y) |
|---------|----------|
|     1     |     2      |
|     2     |     4      |
|     3     |     6      |
  

2. Representation in Roster Form

The roster form lists all ordered pairs of the relation explicitly within curly braces.

Example: R = {(1, 2), (2, 4), (3, 6)}

3. Representation Using Arrow Diagram

An arrow diagram visually connects elements from the domain to their corresponding elements in the range using arrows.

Example:

  Domain     →     Range
    1        →       2
    2        →       4
    3        →       6
  

This is often drawn with two sets of circles and arrows between them:

  {1} → {2}
  {2} → {4}
  {3} → {6}
  

4. Domain and Range of a Relation

• Domain: The set of all first elements (inputs) in the ordered pairs.
• Range: The set of all second elements (outputs) in the ordered pairs.

From the relation R = {(1, 2), (2, 4), (3, 6)}

Domain = {1, 2, 3}

Range = {2, 4, 6}

Summary

• Relations can be represented in multiple forms: tabular, roster, arrow diagram.
• Each representation helps visualize or understand the relationship between two sets.
• The domain consists of all possible inputs, while the range includes all resulting outputs in the relation.