# Practical Work 1 — Set Operations, Venn Diagrams, and Set Algebra

> First practical class of **Computer Discrete Mathematics**. Working **by hand**,
> you illustrate set operations with Euler/Venn diagrams, prove set identities
> with the algebra of sets, and compute concrete sets from set-builder
> descriptions — including a power set.

## At a glance

| | |
|---|---|
| **Topic** | Finite sets: operations, Venn/Euler diagrams, set algebra, power set, inclusion–exclusion, Cartesian product |
| **Prerequisite lectures** | [L01 — Set theory](../../Lectures/CDM-L01.md), [L02 — Set algebra](../../Lectures/CDM-L02.md) |
| **Mode** | In-class problem solving — pen and paper, no computer |
| **Deliverable** | Worked solutions to the tasks in [3classroom.md](3classroom.md) |

## Contents

| # | Part | File |
|:--:|---|---|
| 1 | Objective | [1purpose.md](1purpose.md) |
| 2 | Methodical guidelines (self-contained theory) | [2method.md](2method.md) |
| 3 | Classroom tasks **with solutions** | [3classroom.md](3classroom.md) |
| 6 | Control questions | [6questions.md](6questions.md) |

## Conventions

- **Language** — all work is written in **English**.
- **By hand, from the definitions.** Solve each task using the set definitions
  and the algebra of sets — not a calculator or a computer-algebra tool. The aim
  is fluency with the notation and the laws.
- **Notation is fixed and self-contained.** The symbols $\in$, $\subseteq$,
  $\cup$, $\cap$, $\setminus$, $\triangle$, $\times$, $\overline{A}$, $\varnothing$, and $U$
  are defined in [2method.md](2method.md); no outside reference is needed.
- **State the universe.** A complement $\overline{A}$ only has meaning relative to
  a universal set $U$; whenever a complement appears, $U$ is stated explicitly for
  that problem.
- **Every task has a full solution.** [3classroom.md](3classroom.md) gives each
  task together with a complete worked answer, so the class can check every step.

## Summary

Sets are the foundational language of the whole course. This first practical
turns the definitions of Lectures 1–2 into fluent hand skills: shading the right
region of a Venn diagram, reading a formula back off a diagram, proving an
identity by pushing symbols through the algebra of sets, and computing sets given
by a property. The thirteen tasks progress from **illustrating** operations, through
**proving** two classic identities, to **computing** concrete sets, listing a
**power set**, and finally **counting** with inclusion–exclusion and forming
**Cartesian products** and **symmetric differences** — the exact toolkit relied on
in every later topic, from relations to probability.