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 #

Contents #

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; 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 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.

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