Module 1: Set Theory - MAT 100 - Introduction to College Mathematics - Textbook - LibGuides at Hostos Community College Library

License & Attribution

MAT 100 Introduction to College Mathematics

Compiled by Tanvir Prince

Conditions of Use:

Creative Commons License
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, Ph.D.is licensed under a CC BY-SA 4.0 license.

How to print this page

To print this page:

Click on the printer icon at the bottom of the screen

Is your printout incomplete?

Make sure that your printout includes all content from the page. If it doesn't, try opening this guide in a different browser and printing from there (sometimes Internet Explorer works better, sometimes Chrome, sometimes Firefox, etc.).

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

Sets
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 to understand relationships between groups, and to analyze survey data. This short reading will introduce the basics of set theory.

Assessments

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

Reading Notes

Videos

Assessments

Assessment Sub-Module 2: Operation on Set

Sub-Module 3: Venn diagram

Reading Notes

Venn Diagram
A Venn diagram represents each set by a circle, usually drawn inside of a containing box representing the universal set. Overlapping areas indicate elements common to both sets. Basic Venn diagrams can illustrate the interaction of two or three sets.

Videos

Please watch these videos in the order they are given.

Assessments

Assessment Sub-Module 3: Venn Diagram

Sub-Module 4: Survey

Reading Notes

Survey Questions
Survey 5
Use a Venn diagram and the concepts of cardinal numbers, union and intersection to solve the problem.

Videos

Please watch the videos in the order they are listed.

Assessments

Assessment Sub-Module 4- Survey

Review Exercises for Module 1 : Set Theory

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

Review Exercises for Module 1 - Set Theory

Licenses & Attributions

CC Licensed Content, Original Content

Three ways to write a set. Authored by: Tanvir Prince At: Hostos Community College. License: CC BY 4.0.
Empty Set Elements of Set. Authored by: Tanvir Prince At: Hostos Community College. License: CC BY 4.0.
Subset Proper Subset. Authored by: Tanvir Prince At: Hostos Community College. License: CC BY 4.0.
Assessment Sub-Module 2: Operation on Set. - Questions. Authored by: David Lippman. License: IMathAS Community License (GPL + CC-BY).
Assessment Sub-Module 3: Venn Diagram. - Questions. Authored by: David Lippman. License: IMathAS Community License (GPL + CC-BY).
Assessment Sub-Module 4: Survey. Authored by: David Lippman. License: IMathAS Community License (GPL + CC-BY).

CC Licensed Content, Shared Previously

Sets. Authored by: David Lippman. Located at: http://www.opentextbookstore.com/mathinsociety/. Project: Math in Society. License: CC BY-SA.
Language of sets. Authored by: Timothy Peil, Ph.D. License: CC BY-SA.
Universal set and Venn diagrams. Authored by: Timothy Peil, Ph.D. License: CC BY-SA.
Set operations – unions. Authored by: Timothy Peil, Ph.D. License: CC BY-SA.
Set operations – Intersection. Authored by: Timothy Peil, Ph.D. License: CC BY-SA.
Sets: union, intersection, and complement. Authored by: David Lippman. Located at: https://youtu.be/qTUWzBvI9bk. License: CC BY-SA.
Venn diagram. Found in: Sets. Authored by: David Lippman. Located at: http://www.opentextbookstore.com/mathinsociety/. Project: Math in Society. License: CC BY-SA.
Sets: Drawing a Venn diagram. Authored by: David Lippman. Located at: https://youtu.be/CPeeOUldZ6M. License: CC BY-SA.
Sets: Writing an expression for a Venn diagram region. Authored by: David Lippman. Located at: https://youtu.be/VfC8rhLdYYg. License: CC BY-SA.
Sets: Cardinality. Authored by: David Lippman. Located at: https://youtu.be/wErcETeKvrU. License: CC BY-SA.
Survey Question. Found in: Sets. Authored by: David Lippman. Located at: http://www.opentextbookstore.com/mathinsociety/. Project: Math in Society. License: CC BY-SA.
Sets: Surveys with two sets. Authored by: David Lippman. Located at: https://youtu.be/SKc-gIfPv9o. License: CC BY-SA.
Sets: Surveys with three sets. Authored by: David Lippman. Located at: https://youtu.be/iCDJsOXoySY. License: CC BY-SA.
Review Exercises for Module 1 - Set Theory. Found in: Sets. Authored by: David Lippman. Located at: http://www.opentextbookstore.com/mathinsociety/. Project: Math in Society. License: CC BY-SA.