# 1. Objective / Мета роботи

**Implement the foundational operations on finite sets without using any
pre-built set libraries or classes.**

By the end of the work the student should be able to:

- **represent** a finite set in a chosen programming language using only basic
  data structures (arrays/lists), enforcing the defining property that a set
  contains **no duplicate elements**;
- **implement and test** the core constructors and queries — creation from a
  raw list, insertion, deletion, and membership testing;
- **implement the binary set operations** — union, intersection, and
  difference — and the **complement** with respect to a universal set, matching
  the formal definitions from Lectures 1–2;
- **parse and evaluate** a simple symbolic expression over named sets that
  combines the above operations;
- reason about the **correctness and order-independence** of a set
  implementation and about the **time complexity** of each operation.

The work consolidates the material of
[Lecture 1 — Set theory](../../Lectures/CDM-L01.md) and
[Lecture 2 — Set algebra](../../Lectures/CDM-L02.md) by turning the
definitions into running code.