https://file.aiquickdraw.com/mathbot/file/1727270935970cy14icnl.jpg

The image you uploaded contains a series of math exercises related to sets, relations, and Cartesian products. I'll break down each problem and help you get started on solving them.

### Tugas Pertemuan 3:

**1. Given:**  
\( P = \{2, 3, 4\} \) and \( Q = \{2, 4, 8, 9, 15\} \).  
Define the relation \( R \) from \( P \) to \( Q \) such that \( (p, q) \in R \) if \( p \) divides \( q \) (i.e., \( p \) divides \( q \) exactly).

Tasks:
- **(a) Diagram panah** (Arrow diagram)
- **(b) Pasangan berurutan** (Ordered pairs)
- **(c) Tabel** (Table)
- **(d) Matriks** (Matrix)
- **(e) Diagram Kartesius** (Cartesian diagram)

**2. Given relation:**  
\( R = \{(s,q), (s,r), (p,p), (p,q), (p,s), (q,q), (r,q)\} \).  
Draw the directed graph (graf berarah) from the set of relations.

**3. Given two sets:**  
\( A = \{1, 2, 3\} \) and \( B = \{a, b, c\} \).  
Define the relation from \( A \) to \( B \) with the rule that: "A number from set \( A \) is paired with a letter from set \( B \) if the number is odd."

Tasks:
- **(a) Diagram panah**
- **(b) Pasangan berurutan**
- **(c) Tabel**
- **(d) Matriks**
- **(e) Diagram Kartesius**

**4. Given:**  
\( A = \{1, 2, 3, 4\} \) and the relation \( T \subseteq A \times A \), with the condition that \( T \) holds if and only if the difference between two elements is 1.  
Determine the relation \( T \) and draw the Cartesian diagram.

---

Would you like me to solve any of these problems or explain the process for a specific part? Let me know how you'd like to proceed!

---

Here are 5 follow-up questions to help explore this topic further:
1. How do you determine the relation between two sets in terms of divisibility?
2. What are the common methods to represent relations (e.g., graphs, matrices)?
3. What is the difference between a Cartesian product and a relation?
4. How do you define a directed graph from a set of ordered pairs?
5. How can we visually represent relations in a Cartesian plane?

**Tip:** When working with relations, remember that matrices and graphs provide two different but complementary ways of visualizing the connections between elements of sets!

Misalkan P = {2, 3, 4} dan Q = {2, 4, 8, 9, 15}. Relasi R dari P ke Q dengan (p, q) ∈ R jika p habis membagi q. Buatlah: a) Diagram panah, b) Pasangan berurutan, c) Tabel, d) Matrix, e) Diagram Kartesius. Diketahui relasi R = {(s,q), (s,r), (p,p), (p,q), (p,s), (q,q), (r,q)}. Gambarkan graf berarah dari relasi himpunan R tersebut. Diberikan dua himpunan: A = {1, 2, 3}, B = {a, b, c}. Tentukan relasi dari himpunan A ke B dengan aturan: "Angka dari himpunan A berpasangan dengan huruf dari himpunan B jika angka tersebut ganjil." Buatlah: a) Diagram panah, b) Pasangan berurutan, c) Tabel, d) Matriks, e) Diagram kartesius. Diberikan himpunan A = {1,2,3,4} dan relasi T⊆A×A dengan syarat relasi T berlaku jika dan hanya jika perbedaan antara dua elemen adalah 1. Tentukan relasi T dan gambarkan pada diagram kartesius.

Pelajari bagaimana menentukan relasi antar himpunan berdasarkan divisibilitas, menggambar diagram panah, pasangan berurutan, tabel, matriks, dan diagram Kartesius. Juga, pelajari representasi graf berarah dari relasi himpunan. Cocok untuk siswa kelas 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation