1.5 Set Operations with Three Sets — Double the Complexity | Contemporary Mathematics

Stepping beyond two-set Venn diagrams, this lesson tackles the surprising jump in complexity that happens the moment a third set enters the picture — turning 4 regions into 8 and demanding a whole new strategy. Using vivid real-world examples like blood type compatibility and conference lunch orders, the video walks through how to read, build, and apply three-set Venn diagrams without falling into the trap of double counting. The lesson also introduces the formal grammar of set operations — order of operations, commutative, associative, and distributive properties — and closes with a visual proof of De Morgan's Law. In this video: • How adding a third set doubles the number of Venn diagram regions from 4 to 8 • Reading a three-set Venn diagram using a blood type example (AB+, O–, and 100 donors) • Solving a real compatibility problem: finding Julio's 54 eligible blood donors by filtering out set A • The inside-out (bullseye) method for constructing three-set Venn diagrams without double counting, illustrated with a 50-person conference lunch order • Order of operations for set expressions: parentheses first, then complements, then union or intersection • Commutative, associative, and distributive properties applied to sets • Visual and numerical proof of De Morgan's Law using a universal set of {1–7} #OpenStax #SetTheory #VennDiagram #DeMorgansLaw #ContemporaryMathematics OpenStax Content adapted from "Contemporary Math", by OpenStax Licensed under CC BY 4.0. Content based on Web Version: Apr 23, 2026. Read the textbook online https://openstax.org/details/books/contemporary-mathematics Music first girl talking to me. by ikkun (ex. Barradeen) | https://soundcloud.com/ikkunwastaken Royalty Free Music by https://www.free-stock-music.com Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/by-sa/3.0/deed.en_US