# 1. Objective / Мета роботи

**Gain fluency with the operations and algebra of sets by solving problems by
hand — illustrating operations with diagrams, proving identities, and computing
concrete sets.**

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

- **illustrate** a set expression on an Euler/Venn diagram, shading exactly the
  region it denotes, and conversely **read a formula** back off a shaded diagram;
- **compute** the union, intersection, difference, and complement of concrete
  finite sets, stating the **universal set** whenever a complement is taken;
- **prove a set identity** by two independent methods — a Venn-diagram (region /
  membership) argument and an **algebraic** derivation using the laws of set
  algebra (commutativity, distributivity, complement, and **De Morgan**);
- **translate** between the **roster** form of a set and a **set-builder**
  description, and list a set given by a property (e.g. divisors, primes);
- **construct the power set** $\mathcal{P}(A)$ of a small set and explain why it
  has $2^{|A|}$ elements;
- **count** with the two-set **inclusion–exclusion** principle, and form the
  **Cartesian product** and **symmetric difference** of small sets.

The class consolidates
[Lecture 1 — Set theory](../../Lectures/CDM-L01.md) and
[Lecture 2 — Set algebra](../../Lectures/CDM-L02.md) by exercising
their definitions and laws on concrete problems. All theory needed is restated,
self-contained, in [2method.md](2method.md).