1 PENGERTIAN RELASI - RELASI DAN FUNGSI - KELAS 8 SMP

Summary

This video tutorial introduces the concept of relations and functions in mathematics. It explains how elements from one set can be paired with elements from another set using specific rules, such as color, country flags, shoe sizes, and interests. The video explores three ways to represent relations: arrow diagrams, ordered pairs, and Cartesian diagrams. Examples are provided to illustrate different types of relations, including 'greater than,' 'factors of,' and 'half of.' The lesson concludes with a clear understanding of how to express and visualize relations in various forms.

Takeaways

• 😀 A relation from set A to set B is a rule that pairs elements from A with elements from B.
• 😀 An example of a relation can be a pairing of people and shoe colors, where the rule is the color of the shoe.
• 😀 Another example is a relation that pairs countries with their flags, such as Indonesia with its flag.
• 😀 Relations can be represented in three ways: arrow diagrams, ordered pairs, and Cartesian diagrams.
• 😀 In an arrow diagram, elements from set A are linked to elements from set B based on a specific rule.
• 😀 Ordered pairs represent the relation as pairs of elements, such as (A, 38), (B, 39), etc.
• 😀 A Cartesian diagram pairs set A’s elements on the horizontal axis and set B’s on the vertical axis.
• 😀 Relations can also be described based on preferences or hobbies, such as which students like which sports.
• 😀 A relation can be represented with rules like 'greater than,' where elements from one set are paired with greater elements from another set.
• 😀 Relations can also be formed using rules like 'divisibility' (e.g., 2 is a divisor of 4), which can be expressed as ordered pairs like (2, 4), (3, 6).
• 😀 Relations can also be formed using rules like 'less than' or 'half of,' and these can also be shown with ordered pairs, such as (2, 1), (4, 2), etc.

Q & A

What is a relation in mathematics?

A relation in mathematics is a rule that connects elements from one set (set A) to elements of another set (set B). It defines how elements from the two sets are paired based on a specific criterion.

Can you give an example of a relation using shoes and people?

Yes! A relation can be defined by pairing people with the color of shoes they wear. For example, Woman 1 might wear red shoes, Woman 2 wears blue shoes, and so on. This pairing is based on the color of the shoes.

What are the three methods to represent a relation?

The three methods to represent a relation are: 1) Arrow diagrams, where arrows are drawn between elements of set A and set B; 2) Ordered pairs, where elements are written as pairs like (A, 38); and 3) Cartesian diagrams, where elements are plotted on a coordinate plane.

How does a Cartesian diagram represent a relation?

In a Cartesian diagram, set A elements are placed on the horizontal axis, and set B elements are placed on the vertical axis. The relation is represented by plotting points where elements from both sets are paired.

What is an example of a relation using countries and flags?

An example is pairing country names with their respective flags. For instance, the flag of Indonesia is paired with Indonesia, the flag of Japan with Japan, and so on.

What does 'more than' represent in a relation?

In a 'more than' relation, one number is compared to another, and the relation shows which numbers are greater. For example, 2 is more than 1, 3 is more than 1, and so on.

How is a relation based on factors represented?

A 'factors' relation connects numbers that divide each other evenly. For instance, 1 is a factor of 4, 2 is a factor of 4, and 3 is a factor of 6.

What does a 'less than' relation look like?

In a 'less than' relation, one number is smaller than another. For example, 2 is less than 4, 3 is less than 5, and so on.

Can you give an example of a 'half of' relation?

In a 'half of' relation, one number is half of another. For example, 1 is half of 2, 2 is half of 4, and 4 is half of 8.

What is the purpose of understanding relations in mathematics?

Understanding relations is crucial in mathematics because it helps describe how different sets or elements are connected. Relations form the foundation for more complex concepts like functions, allowing us to understand how input values are mapped to output values.