Himpunan Dasar (Sets)
📌 A set is defined as a collection of clearly identifiable objects, exemplified by students and their favorite foods.
⭐ The Universal Set (S) contains all elements being discussed, while the Cardinality (n(A)) represents the number of elements in a set.
✍️ Sets can be described using three methods: description (words), enumeration (listing members), or set-builder notation.

Jenis Himpunan (Types of Sets)
♾️ Finite Sets have a defined limit to their members (e.g., even numbers up to 20), denoted by ellipses $(\dots)$ if listing is impractical.
🔂 Infinite Sets have members without an upper or lower boundary (e.g., integers extending indefinitely), also using ellipses.
🔢 Set-builder notation reads like: $A = \{y \mid y > 10, y \text{ is a natural number}\}$, where the vertical line means "such that" or "where."

Relasi dan Fungsi (Relations and Functions)
🧩 Both relations and functions involve three components: Domain (input/starting set), Codomain (potential output set), and Range (actual output set/HP).
📉 Relations allow domain elements to have multiple mappings in the codomain or no mapping at all; they are often visualized via Arrow Diagrams.
🎯 Functions require that every domain element has exactly one mapping in the codomain; branching mappings are prohibited.

Fungsi dan Grafik (Functions and Graphs)
📈 The graph of a function should always appear as a curve opening up or down (like a 'U' shape); curves leaning sideways are not graphs of functions.
🔢 Function notation $f(x)$ is used to find output values: If $f(x) = x - 1$, finding $F2$ involves substituting $x=2$ to get $2 - 1 = 1$.
📝 The solution set (HP) for finding $F2=1$ is written as $\{(2, 1)\}$. For multiple evaluations like $G2=7$ and $G3=9$, the HP is $\{(2, 7), (3, 9)\}$.

Korespondensi Satu-satu (One-to-One Correspondence)
🔗 One-to-one correspondence occurs when every element in the Domain maps to exactly one element in the Codomain, and no element is left over in either set.

Key Points & Insights
➡️ The distinction between a relation and a function hinges on the Domain's mapping restriction: one-to-one for functions, free mapping for relations.
➡️ When substituting values into a function like $G(x) = 2x + 3$, the multiplication implied by $2x$ must be calculated first (e.g., $G2 = 2 \times 2 + 3 = 7$).
➡️ Always represent the final answer set (HP) clearly, listing the input and its corresponding output as ordered pairs within curly braces.

📸 Video summarized with SummaryTube.com on Jan 12, 2026, 05:18 UTC