Handouts on SETS, CROSS PRODUCT and COUNTING:

---

VIP: Sets HW clarification and hints, animated GIF presentation, etc. The animation might be very useful.

1. Sets, 3 ways to describe a set, etc.

2. Sets, Cardinality, Subset, Proper Subset, Power Set, etc.

3. Sets, Cartesian Product (Cross Product) and subsets of ...

4. Sets, F*R*I*E*N*D*S who went to same high school, principle of inclusion/exclusion and counting overlapping sets. Review of Cross Product with an example binary relation on FRIENDS cast. Reflexive and Symmetric binary relations preview.

5. Here is a Ghostbuster's problem from section 3.3 of the textbook. We will go over this problem on Tuesday (Wednesday).
   • Overhead slide one with two questions. How many tools are shared by Dr. Peter Venkman and Dr. Egon Spengler is answered here
   • Overhead slide two with Venn diagram and answer to the 2nd question. How many tools does Dr. Egon Spengler use and never share with Dr. Peter Venkman or Dr. Raymond Stantz?

   ---

6. Here is the first page of an old exam from November of 1999. You are ready for many of the problems. The Ghostbusters problem (#1) and PowerSet problems (#2 and #3) and the draw the graph problem (#10) are of special interest as of October 19th.
   1. November 19th, 1999 exam, 1st page key.
   2. Ghostbusters counting problem illustrated solution. The principle of inclusion/exclusion problem solving method is shown, along with a Venn diagram for specific subproblem components.

   ---

7. October 18th, 1999 exam, page 1 with Ghostbusters counting problem (principle of inclusion/exclusion), as well as a proof that the sum of two odd integers has to be an even integer.