Relasi dan Fungsi [Part 1] - Menyatakan Relasi

Introduction

This tutorial provides a clear and concise guide to understanding relations and functions, specifically focusing on how to express relations. The content is based on a lesson aimed at 8th-grade students, making it relevant for those studying mathematics in a remote learning environment.

Step 1: Understand the Concept of Relation

• A relation is a connection between two sets of information.
• It can be represented in various forms, such as:
  • Ordered pairs
  • Tables
  • Graphs
• Key takeaway: A relation shows how elements from one set correspond to elements in another.

Step 2: Learn About Arrow Diagrams

• An arrow diagram visually represents a relation by using arrows to connect elements from one set to another.
• Steps to create an arrow diagram:
  • Identify two sets (e.g., Set A and Set B).
  • Draw circles for each set.
  • Use arrows to connect elements that are related.
• Practical tip: Keep the connections clear and avoid crossing arrows for better visualization.

Step 3: Explore Ordered Pair Sets

• An ordered pair is a pair of elements where the order matters, typically written as (a, b).
• Steps to create a set of ordered pairs:
  • Choose elements from Set A and Set B.
  • Write down the pairs based on the relationships identified.
  • Example: If A = {1, 2} and B = {3, 4}, possible ordered pairs could be (1, 3) and (2, 4).
• Common pitfall: Ensure that each pair is unique within the set.

Step 4: Utilize Cartesian Diagrams

• A Cartesian diagram plots ordered pairs on a graph.
• Steps to create a Cartesian diagram:
  • Set up a coordinate system with an x-axis and y-axis.
  • Plot each ordered pair on the graph.
  • Observe patterns or trends in the plotted points.
• Real-world application: Cartesian diagrams can represent various relationships, such as speed vs. time.

Step 5: Solve Example Problems

• Practice solving problems related to relations and functions.
• Example problem:
  • Given two sets A = {1, 2, 3} and B = {4, 5}, express the relation using an arrow diagram and ordered pairs.
  • Solution: The arrow diagram will show arrows from 1 to 4, 2 to 5, and 3 to a new element if added. The ordered pairs will be (1, 4), (2, 5).

Conclusion

Understanding relations is foundational in mathematics, particularly in the study of functions. This guide has covered the definition of relations, how to represent them using arrow diagrams, ordered pairs, and Cartesian diagrams, as well as practical problem-solving techniques. Next steps could include exploring functions in detail or practicing with more complex examples to deepen your understanding.