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MAT 100 - Introduction to College Mathematics - Textbook

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MAT 100 Introduction to College Mathematics

Compiled by Tanvir Prince


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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

Set operation union image by Timothy Peil, licensed under a CC BY-SA 4.0 license.

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Module 1: Set Theory - Learning Objectives

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

This module is divided into four sections/sub-modules:

Sub-Module 1: Basics of Set. 

  • What is set?
  • Three ways to write a set: "verbal description", "roster form" , "set builder notation"
  • Empty set, element of a set and the corresponding notation
  • Subset and proper subset and its corresponding notation

Sub-Module 2: Union, intersection, complement and universal set. 

  • Union of sets
  • Intersection of sets
  • Complement of sets
  • Universal sets
  • Operation involving all of the above

Sub-Module 3: Venn diagram. 

  • What is Venn diagram and how to draw it
  • How to represent different section in Venn diagram using set notation
  • How to represent set operation using Venn diagram

Sub-Module 4: Survey problem. 

  • Survey questions involving two sets
  • Survey questions involving three sets
  • Advance survey questions

Sub-module 1: Basics of Set

Reading Notes


Sub-module 2: Union Intersection, Complement and Universal Set

Sub-Module 3: Venn diagram

Reading Notes


Please watch these videos in the order they are given.


Sub-Module 4: Survey

Reading Notes



Please watch the videos in the order they are listed. 


Review Exercises for Module 1 : Set Theory

Complete this assessment after you finish all sub-modules in Module 1.

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