Introduction: Set Theory Basics

Learning Objectives

  • Describe memberships of sets, including the empty set, using proper notation, and decide whether given items are members and determine the cardinality of a given set.
  • Describe the relations between sets regarding membership, equality, subset, and proper subset, using proper notation.
  • Perform the operations of union, intersection, complement, and difference on sets using proper notation.
  • Be able to draw and interpret Venn diagrams of set relations and operations and use Venn diagrams to solve problems.
  • Recognize when set theory is applicable to real-life situations, solve real-life problems, and communicate real-life problems and solutions to others.

 
It is natural for us to classify items into groups, or sets, and consider how those sets overlap with each other. We can use these sets understand relationships between groups, and to analyze survey data.