# 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** — the definitions of reflexivity, symmetry, transitivity,
   antisymmetry, an **equivalence relation**, a **partial order**, and the inverse
   of a relation, in your own words (see [Lecture 3 — Relations](../../Lectures/CDM-L03.md)).
4. **Chosen representation** — how a relation and the underlying set are stored,
   and how a pair is looked up (membership test).
5. **Implementation** — the source code of each check (`isReflexive`,
   `isSymmetric`, `isTransitive`, `isAntisymmetric`, `isEquivalence`,
   `isPartialOrder`) and of `inverse`, with brief comments. State the programming
   language used.
6. **Testing** — for each function, a table of inputs and results including the
   examples of [4task.md](4task.md) **and** your own cases: a relation that fails
   each property (e.g. a non-symmetric or non-transitive one) so that both `True`
   and `False` outcomes are demonstrated.
7. **Achieved band** — state which band you reached and which tasks it covers.
8. **Complexity** — the time complexity of each check and how it changes with a
   hash-based membership test.
9. **Conclusions** — what was implemented, difficulties encountered, and what you
   learned about the properties of relations.

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