Daily Prep 3.2 – MTH 225

Overview

In this lesson, we'll build on our new concept of sets to determine when one set is a subset of another or equal to another, and learn the set operations of union, intersection, complement, difference, symmetric difference, and Cartesian product. We'll also learn the concept of cardinality of a set and how to form the power set of a set.

Learning objectives

Basic Learning Objectives: Before our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught.

• State the definition of "subset" and given two sets, determine if one is a subset of the other.
• State the definition of "equality" of sets, and given two sets, determine if they are equal.
• Given a finite set, write its power set.
• Given a finite set, state its cardinality.
• Given two sets, find their intersection, union, difference, symmetric difference, and Cartesian product.
• Given a set and its universal set, find its complement.

Advanced Learning Objectives: During and after our class meeting, we will work on learning the following. Fluency with these is not required prior to class.

• Use Venn diagrams to make conjectures about combinations of set operations and then give explanations for why the conjecture is true.

Resources for learning

Video: Watch these from the MTH 225 playlist (total running time 25:29):

Screencast 3.6: Set operations from Robert Talbert on Vimeo.

Text:

You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below.

Exercises

Once you have watched the videos above, go to this form and complete all the non-optional items on it:

https://docs.google.com/forms/d/e/1FAIpQLScv7SMR9SEdrkjq-eYvrI2H97DWLDMVgh-1A9cYF02-T95wXg/viewform

Submission and grading

Submitting your work: Your work is submitted when you submit the Google Form. You should receive an email receipt indicating that the work was submitted successfully.

How this is graded: The pre-class portion of the Daily Prep is graded either 0 points or 1 point, on the basis of completeness and effort. Wrong answers are not penalized. Earning a "1" requires that you:

• Turn the work in before its deadline;
• Leave no item blank or skipped, even accidentally; and
• Give a good-faith effort at a correct answer on every non-optional item.

More information can be found in the Specifications for Satisfactory Work in MTH 225 document.

When you arrive for the class meeting, you'll be put into a group of 2-3 to complete a quiz over this material, which will be graded on a 0/1 scale on the basis of correctness.