**Week 1**

Create a star "venn diagram" on the circle paper in which either 3,4, or 5 regions are colored. All regions with the same code, i.e., 011 or 101, etc. are give the same color. Translate your diagram into a truth table where the colored regions are true and the uncolored are false values of the statement.

Extra credit: create and interesting star diagram using color.

page 8/1-4,

page 23/1a,b,c,2-5,10a, 11c,d

Handout: 7,8,9

To do problem 9 of the the handout you should note that there are several different translations

of p-->q. Here they are:

if p then q

if p, q

p is sufficient for q

q if p

q whenever p

q is necessary for p

q follows from p

p implies q

p only if q

**Week 2**

9/11

Read the handout on the "new logic"

Use a truth table with the mark to show that the truth table for (not p or q) gives you the same result as

p-->q

* Show using the new Boolean algebra that : (p and (p-->q))-->q = 1

*show using the new Boolean algebra that r-->(p-->q) = (r and p) --> q

Use the new Boolean algebra to do: Section 1.2 / 2a, 4, 5a

Use truth tables with the mark and the blank to do Sec. 1.2/ 2a,4,5a

Remember that a^{n} = a where n is any positive integer.

Do the handout problem 47 (another consistency problem)

9/15

29/3a*,5c*,f,d (do this for extra credit), 6*

Prove: ((p-->q) and (q-->r)) --> (p--r) = T (hypothetical syllogism)

Do Ladies Luncheon problem from classnotes (for extra credit)

Come to the Technology and society Forum on Wed. and tell your friends about it.

9/18

Do ladies luncheon problem for extra credit

On handout do:

12* a,b, f) (at top of page), 11 a,c* (use my shortcut method)

in the book for problem 30/10f * a) create the truth table by using boolean arithmetic, b) use the new boolean algebra to find the logic gates necessary to implement this function using 1) nand and not gates 2) nor and not gates

9/22

On handout do: 12 c,d, 11b, problem g at the top of the page

Diagram syllogisms 9 and 10

Do 30/ 10 b draw the K-map and draw the gate diagrams with not and nor gates for the original logic statement and the simplified K-map.

34/ 3a,b,c

Read about quantifiers on page 5 and 6 and do problem on page 9/ 7a-h

I would like you to write a two page essay responding to Essay 1 on the M226 class notes on the web.

Short quiz on Thursday

9/25

Read Section 2.1 and do:

1,3,5,7,9

Bring in your essay.

9/28

Please read Sections 2.1 and 2.2. I will send the hw problems to you later in an e-mail.

**Week 5**

10/2

Do 2.3/1,2

Read chapter and try to do 2.3/3

Study for exam** **which will cover Sections 1.1, 1.2, 1.3, 2.1, 2.2

**Week 6**

10/9

I will send your homework through the e-mail. If you don't get it please e-mail me.

10/13

2.4/ 1,2,7,9,12, from last assignment and 2.4/13,14,15,16,17,19,21,23 from today

2.5/1,3,4

Draw the Hasse diagram for the partially ordered relation: (A, | ) where A = {2,4,5,10,12,20,25 } and

aRb iff a|b .

Last chance to draw a Venn diagram with four sets.

10/20

3.1/ 1, 2, 3,4,12, 13,15,16,17,21,28,30

**Week 8**

10/23

3.1/9*, 10*, 11* * means extra credit

3.2/1, 3, 6,7a,c, 810,, 11 a,b,c15, 18,20,26,28

Choose a pair of two digit integers and and find their product by the "Sumerian" method that I showed in class today. For this same pair prove that the multiplication and addtion of them are correct by using the tricky addition method I showed in class today.

Study the proof of the division algorithm that is shown in the book. It is based on the well ordered property of integers that says that and set of integers that is bounded from below has a smallest element.

10/28

4.1/5, 8, 9, 11

4.2/ 2, 3,4, 5*,6*,7*, 10c, 12a,d,19, 14 (read the solution)

Week 9

10/30

Section 4.2 /8, 10e,11,12e, 16,17,23,27,35

Draw some interesting 8 and 12 pointed stars and color them to demonstrate that {n,p} can be drawn without lifting your pencil when n and p are relatively prime.

I forgot to mention that there is an interesting conference sponsored by the technology and society forum tomorrow morning (Friday Oct 31) from 8:30 - 1 PM in the Student Center Atrium on the Future of Broadband. Several big companies like ATT, Verizon, Viugin, and Comcast will be making presentations. You might find this interesting.

11/3

4.4/ 3, 6, 9a-g, 10, 11a,b,14, 18,, 21a,b,c

Prove the Theorem: ac=bc mod mc -> a = b mod m

Don't forget to vote

**Week 10**

11/6

4.5/1,2a,b,c,3,9a,b,c, 10a, 18a,c,d,g, 21a

Solve the chinese remainder problem that I gave in class with mod 7,11,13

The exam will cover : relations, functions, and integers, and modular arithmetic

**Week 11**

11/14

Section 5.1/ 4a, c, g, j, k, 5, , 6a, e, 8a, , 9a, c, e

11/17

5.2/1, 2, 3 (prove by induction), 7, 8, 9,12,15,18,25, 26,33, 39*,45, 47, 52, 53

Prove by induction that you can tile any integral length 12 or greater by planks of length 3 and 7.

Hand in two page essay 2 by next Monday.

**Week 12**

5.3/1,3,11,12,13,15

Essay 2 from class notes is due Monday

Do the problems from the previous homework if you have not already done so. Also do 5.2/33,34

11/25

6.2/ 1-7,9,11,15,16,20,21,23,25,26

These problems are challenging, but you will only need the sum and product rules and counting tree from you counting toolkit. Also the thinking cap will be invaluable. We will discuss them next week. Have a good thanksgiving. Prof. Kappraff

**Week 14**

Here some problems from 7.2 and 7.3. Do as many as you have time for and we will work on he rest in class on Thursday

7.1/1,3,5,7,9,10,12,15,16

7.2/ 1,3,6,8,10,12,13, 17,20,21,22