Sets and Operations on Sets Using Venn Diagrams

About this course

A comprehensive, highly structured 100-level university course in Set Theory. Designed for STEM students taking Elementary Mathematics (MTH 101 / MAT 101), covering elements, membership symbols (∈, ∉), roster and set-builder notation, cardinality, subsets, power sets, universal sets, complements, union, intersection, disjoint sets, set difference, symmetric difference, algebraic laws of sets, De Morgan's laws, and a dedicated final chapter with graduated calculation problems solved from center outward with high-resolution Venn diagrams.

What you'll learn

• Master set membership notation ($x \in A, x \notin A$) and translate fluently between Roster and Set-Builder forms
• Calculate set cardinality $n(A)$, identify empty sets ($\emptyset$), and determine power sets with the $2^n$ formula
• Execute core set operations: Union ($A \cup B$), Intersection ($A \cap B$), and Relative Complement ($A \setminus B$)
• Apply and prove fundamental set algebraic identities including De Morgan's Laws ($(A \cup B)' = A' \cap B'$)

Prerequisites

• Basic high school arithmetic and elementary algebra (linear equations and positive/negative integers)
• No previous university mathematics or advanced calculus required