Set+Language+and+Notation

=**Assessed Task(s)**:= =** Set and Venn Diagram Unit Test (Criterion A) **=

TYPES OF PROBLEMS YOU WILL NEED TO SOLVE:

 * ===**Tell whether a set is well defined.**===
 * === ****Specify sets by roster and by description.**** ===
 * === ****Understand and use set-builder notation.**** ===
 * === ****Draw Venn diagrams showing subsets, equal sets, or disjoint sets.**** ===
 * === ****Distinguish between equal and equivalent sets, and find the cardinality of a given set.**** ===
 * === ****Distinguish the symbols for subset, proper subset, and element.**** ===
 * === ****Find the complement of a set.**** ===
 * === ****Find the union of two sets.**** ===
 * === ****Find the intersection of two sets.**** ===
 * === ****Recognize and draw the Venn diagrams for union, intersection, and complement.**** ===
 * === ****Solve survey problems involving two sets.**** ===
 * === ****Perform mixed operations using union, intersection, and complement**** ===
 * === ****Draw Venn diagrams for mixed operations using union, intersection, and complement.**** ===
 * === ****Draw Venn diagrams using three or more sets.**** ===
 * === ****Prove or disprove set statements using Venn diagrams.**** ===
 * === ****Solve survey problems involving three or more sets.**** ===
 * === ****Find the Cartesian product of two sets, and determine its cardinality.**** ===
 * === ****Find the cardinality of a given set.**** ===
 * === ****Determine whether sets have the same cardinality by placing them in a one-to-one correspondence.**** ===
 * === ****Classify a given set at finite or infinite.**** ===
 * === ****Show that a given set has cardinality aleph null.**** ===
 * === ****Show that a given set is infinite.**** ===

Venn Diagrams (2:00)



 * Georg Cantor:**
 * http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Cantor.html**




 * John Venn:**
 * @http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Venn.html**

**Reference Topic Sites:**

**This is a general review of the material of this section.** ** @http://library.thinkquest.org/C0126820/setsubset.html **


 * This site is a general introduction to sets. **
 *  @http://www.math.uncc.edu/~droyster/math3181/notes/hyprgeom/node8.html **

**Basic concepts and notation for sets: **
 * @http://www.math.utah.edu/~alfeld/math/sets.html **

**This site reviews sets and set notation: ** ** http://www.math.csusb.edu/notes/sets/node1.html#SECTION00010000000000000000 **

**Reference Topic Sites:**

 * This is a web-based instructional module on the algebra of sets.**
 * @http://lrs.ed.uiuc.edu/students/avilesga/project/main.html**

**Union of Sets: ** **@http://lrs.ed.uiuc.edu/students/avilesga/project/union.html **

**<span class="text" style="color: #0000p0; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">Intersection of Sets: ** <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**<span class="text" style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">@http://lrs.ed.uiuc.edu/students/avilesga/project/intersection.html **

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**<span class="text" style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">Venn Diagrams for union and intersection: ** <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**<span class="text" style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">@http://lrs.ed.uiuc.edu/students/avilesga/project/venn.html **

**Reference Topic Sites:**

 * This site gives some interesting practice with combined operations with sets:**
 * @http://ww2.unime.it/dipart/i_fismed/wbt/mirror/moe/tests/mengen/duv.html**

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**Venn diagrams with two, three, and four sets:**
 * If you click on the question mark, you can practice with three overlapping sets.**
 * @http://www.math.csusb.edu/notes/sets/node5.html**


 * <span class="text" style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">This site shows a statement of De Morgan's law. **
 * <span class="text" style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">@http://www.demorgan.com/demorgan.htm **

**Video**:

 * Infinity. (time: 9:42)**
 * The smallest Infinity (time: 9:33)**

**Reference Topic Sites:**

 * This site introduces the idea of infinite sets:**
 * @http://mathforum.org/isaac/problems/cantor1.html**

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**<span class="text" style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">This site introduces the idea that there are different sizes of infinity: ** <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**<span class="text" style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">http:http://personal.bgsu.edu/~carother/infinite/Infinite1.html **

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**<span class="text" style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">"A Crash course in the Mathematics of Infinite Sets," by Peter Suber, Earlham College: ** <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**<span class="text" style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">@http://www.earlham.edu/~peters/writing/infapp.htm **