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

Summary

This 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.