Relations and Their Representations
A binary relation from $A$ to $B$ is a subset $R \subseteq A \times B$.
Summary
A binary relation from to is a subset . It identifies which ordered pairs are connected, without requiring the single-output restriction of a function. In computing, relations model web links, database associations, dependencies, and state transitions.
Finite relations can encode the same membership information in different forms:
| Representation | Membership encoding |
|---|
🧠 Key Concepts
- Ordered pairs
- Cartesian product
- Boolean matrix
- Directed graph
- Inverse relation
- Relation composition
- Domain and range
- Reflexivity
- Symmetry
- Transitivity
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A relation models links from source pages to destination pages. What does indicate in its Boolean matrix?
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Relations and Their Representations
📘 Overview A binary relation specifies which ordered pairs connect elements of two sets. Finite relations can be represented by sets of ordered pairs, Boolean matrices, or directed graphs, making the same connections available for different computational tasks.
🧠 Key Idea A relation is a set of ordered pairs; its representations encode the same membership information. A listed pair, a matrix entry of one, and a directed edge all indicate that a connection belongs to the relation.
⚔️ Core Details: - A binary relation from to is any subset
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Part of 🌱 BSCS Year 1 — Computing & College Foundations
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