Set theory: Venn diagrams, notation, union, intersection and complement

This week’s topics

Set theory: Venn diagrams, notation, union, intersection and complement

1. Set theory: Venn diagrams, notation, union, intersection and complement
2. Boolean identities linking logic and set algebra

What you will be able to do

• 2.2 Describe the possible algebraic operations in set theory.
• 2.5 Analyse the similarities between Boolean logical operators and Boolean algebra in set theory.

Activity

Start with this week’s 4 videos, then: Seminar, guided reading and a short written task: describe the possible algebraic operations in set theory.

Study materials

Videos

• Set notation · Oak National Academy, Key Stage 4 (GCSE level) · for registered students
• Using a Venn diagram to display outcomes for two events · Oak National Academy, Key Stage 3 (lower secondary level) · for registered students
• Intersection of Sets, Union of Sets and Venn Diagrams · YouTube · The Organic Chemistry Tutor · 12 min · for registered students
• Algebra 3 - Venn Diagrams, Unions, and Intersections · YouTube · MyWhyU · 6 min · for registered students

Further resources

• Contemporary Mathematics, 1.1: Basic Set Concepts · PDF · OpenStax Contemporary Mathematics (2023), 1.1: sets, elements and set notation, pp. 6–13 · for registered students
• Contemporary Mathematics, 1.3–1.4: Venn diagrams and set operations · PDF · OpenStax Contemporary Mathematics (2023), 1.3–1.4: Venn diagrams, union, intersection and complement, pp. 20–39 · for registered students
• Contemporary Mathematics, 2.6: De Morgan's Laws · PDF · OpenStax Contemporary Mathematics (2023), 2.6: simplifying Boolean expressions with De Morgan's laws, pp. 102–107 · for registered students
• A survey of Euler diagrams · Open-access article · Rodgers (2014), Journal of Visual Languages & Computing. Survey of Euler and Venn diagrams and how they represent sets. · for registered students