Relasi dan Fungsi (1) | Menyatakan Relasi | Matematika Kelas 8

Kimatika

11 Oct 202111:56

Summary

TLDRThis video from the 'kinematika' channel offers a comprehensive lesson on the concept of relations and functions in 8th-grade mathematics. It explains what a relation is, as a connection between elements of two sets, using the example of Indonesian provincial capitals and provinces. The video demonstrates three ways to express relations: through an arrow diagram, ordered pair set notation, and a Cartesian diagram. It also includes examples of how to represent these relations, such as the reading preferences of individuals and mathematical relationships like squares and roots. The lesson concludes with exercises to practice identifying and expressing relations, making the content both informative and interactive.

Takeaways

📚 Introduction to class 8 mathematics material on relations and functions.
🧩 Definition of relation: the relationship between members of different sets.
🔢 Example using sets of provincial capitals in Indonesia starting with 'S' and provinces on Java island.
🏙️ Specific pairs: Semarang with Central Java, Surabaya with East Java, and Serang with Banten. Samarinda has no pair as it is in Kalimantan.
🔄 Relations are connections between members of two sets, not all members must have pairs.
📊 Three ways to express relations: arrow diagram, ordered pair set, and Cartesian diagram.
📝 Example of a relation between people and their preferred reading materials using different methods.
📐 Arrow diagram: connecting members of one set to another with arrows.
📝 Ordered pairs: writing pairs in curly brackets and parentheses.
📉 Cartesian diagram: plotting relations on a graph with horizontal and vertical axes.
📚 Example problem: determining the correct relation type from a given arrow diagram.
📈 Example problem: creating ordered pairs from a Cartesian graph.

Q & A

What is the main topic discussed in the video?
-The main topic discussed in the video is the concept of relations and functions in mathematics for 8th-grade students, specifically focusing on what a relation is and how to express it.
What is a relation in the context of sets?
-A relation is a connection between members of one set with members of another set. It is a way to pair elements from set A with elements from set B.
What are the two sets used as examples in the video to explain relations?
-The two sets used as examples are set A, which contains the capitals of provinces in Indonesia starting with the letter 'S', and set B, which contains the provinces on the island of Java.
How many ways are mentioned in the video to express relations?
-Three ways to express relations are mentioned in the video: using an arrow diagram, ordered pair sets, and a Cartesian diagram.
What is an ordered pair set (Himpunan Pasangan Berurutan)?
-An ordered pair set is a way to express relations by listing pairs of elements from two sets, where the first element of each pair is from the first set and the second element is from the second set.
How is a Cartesian diagram used to represent relations?
-A Cartesian diagram is used to represent relations by placing elements of one set on the horizontal axis (x-axis) and elements of the other set on the vertical axis (y-axis), and then drawing lines to connect related elements.
What is an example of a relation given in the video?
-An example of a relation given in the video is the relation between a group of children (Irma, Dewi, and Ani) and a group of reading materials (magazines, comics, and novels), where the relation is 'likes to read'.
How is the relation 'likes to read' expressed in an arrow diagram?
-In an arrow diagram, the relation 'likes to read' is expressed by drawing arrows from the children to the reading materials they like, such as from Irma to 'magazine', from Dewi to 'comic', and from Ani to 'novel'.
What is the significance of the example with the numbers 1, 2, 3, 4, and 5 in the video?
-The significance of the example with the numbers is to illustrate how to determine the correct relation from a given arrow diagram, where the relation is 'square of', and to show how to answer a multiple-choice question based on that diagram.
How is the relation 'one less than' expressed in the ordered pair set format?
-The relation 'one less than' is expressed in the ordered pair set format by listing pairs where the first number is one less than the second number, such as (2, 3), (5, 6), and so on.
What is the final example in the video about?
-The final example in the video is about expressing the relation 'one less than' between the set P containing the numbers 2, 5, 7, and 9, and the set Q containing the numbers 3, 6, 8, and 10, using the ordered pair set format.

Outlines

00:00

📚 Introduction to Relations and Functions in Mathematics

This paragraph introduces the topic of relations and functions in the context of 8th-grade mathematics. It explains the concept of a relation as a connection between members of one set with another set, using the example of Indonesian provincial capitals starting with the letter 'S' and provinces on the island of Java. The paragraph also discusses how to express relations using three methods: arrow diagrams, ordered pair sets, and Cartesian diagrams. An example is given to illustrate these methods, involving a group of children and their reading preferences for different types of books.

05:01

📈 Expressing Relations with Ordered Pair Sets and Cartesian Diagrams

The second paragraph delves deeper into the representation of relations using ordered pair sets and Cartesian diagrams. It provides a step-by-step explanation of how to write relations in the form of ordered pairs, using the example of individuals and their reading preferences. The paragraph also explains how to create a Cartesian diagram to represent these relations, including how to label the axes with the members of each set and connect them with lines to show the relationships.

10:03

🔍 Solving Relation Problems Using Diagrams and Ordered Pair Sets

The final paragraph presents a practical application of the concepts discussed in the previous sections by solving problems related to relations. It includes a multiple-choice question about identifying the correct relation from an arrow diagram and a task to create an ordered pair set from a given Cartesian diagram. The paragraph also provides an example of expressing a relation from set P to set Q using the 'one less than' relationship, demonstrating how to form the ordered pair set accordingly.

Mindmap

Keywords

💡Relation

A 'relation' in mathematics refers to the connection between elements of one set and another. In the video, the concept is central to understanding how different sets of data or objects can be associated with one another. For example, the script discusses the relationship between the set of Indonesian provincial capitals starting with 'S' and the set of provinces in Java, illustrating how each capital is paired with its respective province.

💡Function

While not explicitly defined in the script, 'function' is a mathematical concept closely related to relations. A function represents a specific kind of relation where each element of one set (domain) is paired with exactly one element of another set (codomain). The script's discussion of relations lays the groundwork for understanding functions, which could be the topic of a subsequent video.

💡Set

A 'set' is a collection of distinct objects, considered as an object in its own right. In the video, sets are used to organize data, such as the set of Indonesian capitals starting with 'S' and the set of provinces in Java. The script uses sets to demonstrate the concept of relations, showing how elements within sets can be related to each other.

💡Diagram of Arrows

A 'diagram of arrows' is a visual representation used to depict relations between elements of two sets. The script describes how to use arrows to connect members of one set to members of another, indicating the relationship between them. For instance, it explains how to represent the reading preferences of individuals using arrows to connect them to the types of reading materials they prefer.

💡Ordered Pair

An 'ordered pair' is a pair of elements where the order is significant, often used to represent elements of a relation. The video script explains how to express relations using ordered pairs, such as (Irma, Magazine) to indicate that Irma prefers to read magazines, which is a way to concisely represent the relation between individuals and their preferences.

💡Cartesian Diagram

A 'Cartesian Diagram' is a graphical representation of ordered pairs in a coordinate system, typically used to visualize relations. The script describes how to use a Cartesian diagram to represent the reading preferences of individuals, placing individuals on one axis and types of reading materials on the other, and then drawing lines to connect related items.

💡Himpunan

The term 'himpunan' is Indonesian for 'set'. The script uses this term to discuss the elements that are part of a relation, such as the set of provincial capitals or the set of provinces in Java. Understanding 'himpunan' is crucial for grasping the script's explanation of relations and their representation.

💡Pasangan

In the context of the script, 'pasangan' is Indonesian for 'pair', which is used to describe the pairing of elements from two different sets in a relation. The script explains how to identify and represent these pairs in different ways, such as in a diagram of arrows or a Cartesian diagram.

💡Gemar Membaca

'Gemar Membaca' is Indonesian for 'fond of reading' or 'likes to read'. The script uses this term to describe a relation between individuals and their reading preferences, such as magazines, comics, or novels. It is an example of how a relation can be expressed in a real-world context.

💡Majalah, Komik, dan Novel

These terms, which translate to 'magazine', 'comic', and 'novel', are used in the script to represent different types of reading materials. They are part of the set of elements that individuals may be related to through their reading preferences, serving as examples of how relations can be established between sets.

💡Satu Kurangnya

'Satu Kurangnya' is a phrase used in the script to describe a specific type of relation where one element is one less than another. It is used to illustrate how to express relations in the form of ordered pairs, such as '2 one less than 3', which would be represented as (2, 3) in the context of the video.

Highlights

Introduction to the concept of relations and functions in 8th-grade mathematics.

Definition of a relation as a relationship between members of two sets.

Explanation of how to represent a relation using three different methods.

Example using the capitals of provinces in Indonesia starting with 'S' and provinces on the island of Java.

Illustration of how to connect members of two sets using the relation 'capital of'.

Clarification that not all members from both sets must have a pair in a relation.

Introduction to the notation for a relation from set A to set B.

Use of an arrow diagram to represent the relation between individuals and types of reading materials.

Explanation of how to create an ordered pair set (Himpunan Pasangan Berurutan) to express the relation.

Demonstration of how to use a Cartesian diagram to visually represent the relation.

Solution to a multiple-choice question about identifying the correct relation from an arrow diagram.

Guidance on creating an ordered pair set from a Cartesian diagram.

Example of expressing the relation between sets P and Q using the ordered pair set method.

Explanation of the 'one less than' relation in the context of set theory.

Solution to a problem involving finding the 'one less than' relation between two sets of numbers.

Conclusion and final thoughts on understanding relations and their representations in mathematics.