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 of a small set and explain why it has 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 and Lecture 2 — Set algebra by exercising their definitions and laws on concrete problems. All theory needed is restated, self-contained, in 2method.md.