# Laboratory Work 2 — Cartesian Products and Relations

> Second laboratory work of **Computer Discrete Mathematics**. You implement the
> **Cartesian product** of sets from first principles, then build on it to test
> and generate **binary relations** — including relations defined by a predicate
> and filtered products.

## At a glance

| | |
|---|---|
| **Topic** | Ordered pairs, Cartesian product, binary relations as subsets of $A\times B$ |
| **Prerequisite lectures** | [L02 — Set algebra](../../Lectures/CDM-L02.md), [L03 — Relations](../../Lectures/CDM-L03.md) |
| **Deliverable** | Source code + report (see [5report.md](5report.md)) |
| **Grading** | Banded: Easy 60–74 / Medium 75–89 / Hard 90–100 (see [4task.md](4task.md)) |

## Contents

| # | Part | File |
|:--:|---|---|
| 1 | Objective | [1purpose.md](1purpose.md) |
| 2 | Methodical guidelines (theory & algorithms) | [2method.md](2method.md) |
| 4 | Task and order of execution | [4task.md](4task.md) |
| 5 | Report contents | [5report.md](5report.md) |
| 6 | Control questions | [6questions.md](6questions.md) |

## Conventions

- **Language** — source code and the report are in **English**.
- **Implement it yourself — no built-in shortcuts.** Do not call a library or
  built-in that performs the core task for you (e.g. no `HashSet`/`set()`/`Set`
  for sets, no library graph/relation type, no `math.gcd`, no `eval`). Build the
  mechanism from basic primitives — arrays/lists, loops, arithmetic, strings.
- **Deliverable** — submit the source code **and** a report structured as in
  [5report.md](5report.md); the code must reproduce the example outputs in
  [4task.md](4task.md).
- **Self-contained theory** — everything needed is in [2method.md](2method.md);
  no external material is required.

## Summary

The **Cartesian product** $A\times B$ is the set of all ordered pairs drawn from
two sets, and a **relation** is simply a subset of such a product. This makes the
product the foundation for everything relational in the course — functions,
orders, equivalences, and graphs are all special kinds of relations. In this work
you generate products by hand, check that a candidate relation really lives
inside $A\times B$, generate relations from a predicate, and filter a product to
the pairs that satisfy a condition. The work is graded in three tiers of
increasing difficulty.