# 5. Report contents / Зміст звіту

The report is submitted together with the source code. It must contain the
following sections.

1. **Title block** — course, laboratory work number and title, student's name
   and group, date.
2. **Objective** — a short statement of the goal of the work (see
   [1purpose.md](1purpose.md)).
3. **Brief theory** — ordered pairs, the Cartesian product $A \times B$, and the
   definition of a binary relation as a subset of $A \times B$, in your own words
   using standard relation notation (see
   [Lecture 3 — Relations](../../Lectures/CDM-L03.md)).
4. **Chosen representation** — how an ordered pair and a product/relation are
   stored without built-in set/tuple helpers, and how components are compared.
5. **Implementation** — the source code of every implemented function, with
   brief comments. State the programming language used.
6. **Testing** — for each function, a table of test cases and results. Include
   the examples from [4task.md](4task.md) **and** your own edge cases: an empty
   factor ($A \times \varnothing$), the size check $|A \times B| = |A|\cdot|B|$,
   a relation that is **valid** and one that is **invalid**, and a predicate that
   selects no pairs.
7. **Achieved tier** — state the highest tier you completed and which functions
   it covers (see the grading bands in [4task.md](4task.md)).
8. **Complexity** — the time complexity of `cartesianProduct`, `isRelationValid`,
   `findRelations`, and `filteredCartesianProduct`, with one sentence on how a
   hash-based membership test would affect validation.
9. **Conclusions** — what was implemented, the difficulties encountered, and what
   you learned.

**Submission requirements.** The source files must compile/run and reproduce the
example outputs of [4task.md](4task.md).