---
tags: mth225, dailyprep
---

# 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](https://vimeo.com/showcase/8667148) (total running time 25:29):

<iframe src="https://player.vimeo.com/video/606554057?h=367ebde300" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe>

<iframe src="https://player.vimeo.com/video/606573917?h=e0ea25ff64" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe>

<iframe src="https://player.vimeo.com/video/606600971?h=e256db4c8a" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe>
<p><a href="https://vimeo.com/606600971">Screencast 3.6: Set operations</a> from <a href="https://vimeo.com/user132700952">Robert Talbert</a> on <a href="https://vimeo.com">Vimeo</a>.</p>

<iframe src="https://player.vimeo.com/video/606627934?h=0a0e06f5a8" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe>

**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](/Cy6P0rGZQzuOM3NwZ3ZuMw) 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.