Course Goals and Anticipated Outcomes for This Chapter:
Develop the student:
- ability to understand the basic knowledge of set theory,
- familiarity and facility with a wide range of set-theoretical statements and the connection to K-9 curriculum, and
- reasoning using Venn diagrams and proofs.
- 2.0: Introduction
- 2.1: Subsets and Equality
- Sets can be arranged into smaller groups called subsets. Sets can also be equal to, each other.
- 2.2: Operations with Sets
- The relative complement of A with respect to a set B, also termed the difference of sets A and B, written B ∖ A, is the set of elements in B but not in A. When all sets under consideration are considered to be subsets of a given set U, the absolute complement of A is the set of elements in U but not in A.
- 2.3: Properties of Sets
- The following set properties are given here in preparation for the properties for addition and multiplication in arithmetic. Note the close similarity between these properties and their corresponding properties for addition and multiplication.
- 2.4: Venn Diagrams and Euler Diagrams
- A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves.
- 2.E: Basic Concepts of Sets (Exercises)