Mat200/Proof Writing Through Discrete Mathematics Assignments-Fall 2014

All assignments are for the Fourth Edition

Assignment

Carefully read all sections of my web page for this course, particularly the grading policy.

.....due 8-27-2014 .....

Note: "tba" means "to be announced"

Note: Specific due dates are for reference only

and should be used to keep your study habits/plans on track

Assignment

Read Sections 2.1, 2.2 & 2.3

.....Section 2.1 Problems 1,3,6,14, ,16,18 & 21

.....Section 2.2 Problems 3,5,9,16,22,23 & 29

.....Section 2.3 Problems 1,5,6,9,12,38a,41 & 42

...............Due 9-3-2014...............

Assignment

Read Sections 3.1, 3.2, 3.3 & 3.4

......Section 3.1 Problems 1,3,6,9,13,19 & 28 .........

......Section 3.2 Problems 1,3,17.........

......Section 3.3 Problems 1,3,14,15,18,31,41a,b,c.....

......Section 3.4 Problems 2,3,4,10,13,17,21 & 23 .....

a) Prove that For all x in Z, if x is in 3Z+1 or x is in 3Z+2 , then x^2 is not in 3Z

b) State the contrapositive of the theroem in a)

c) Prove that Sqrt(3) is not in Q (Hint: use Theorem in b)

......due 9-19-2014......

Assignment

Read Sections 4.1, 4.2, 4.3, 4.4, 4.6, 4.7 & 4.8

Section 4.1 Problems 1,2,3,4,6,8,9,11,24,25,27,38,39 & 40 ...

........Section 4.2 Problems 3,4,6,8,12,18 & 21.........

........Section 4.3 Problems 1,4,5,8,14,26,29 & 38.........

........Section 4.4 Problems 1,3,5,7,9,17,19,21 & 23.........

........Section 4.6 Problems 5,7,9b,20,31a.........

Use the contrapositive of the if...then statement in 31b to conclude that if a positive integer n is not divisible by a prime that is <= sqrt(n), then n is a prime number. Also, use 31b as stated and the theorem proved in class that any composite integer n can be expressed as the product of primes in the form p1*p2*....*pk (listed in increasing order) to conclude that p1 <= sqrt(n), p2 <= sqrt(p2p3..pk) <= sqrt(n) , etc , p(k-1) <= sqrt (p(k-1)pk) <= sqrt(n). Because of this observation, therefore p2, p3, ...., p(k-1) also must be less than sqrt(n). However, pk does not have to be less than sqrt(n) as the simple example 14 = 2*7 illustrates. since 7 is not <= sqrt(14).

........ & 32 ..................................

........Section 4.7 Problems 1,3, 19 extra credit & 23.........

........Section 4.8 Problems 13 & 15.........

......due 10/3/2014 .......

Assignment

Read Sections 5.1, 5.2, 5.3 & 5.4

Section 5.1 Problems 1,2,3,4,6,8,9,11,24,25,27,38,39 & 40 ...

........Section 5.2 Problems 8,9,12 & 15.........

........Section 5.3 Problems 6,8 & 16.........

........Section 5.4 Problems 1,3,5 & 13.........

......due 10/10/2014 .......

Assignment

Read Sections 6.1, 6.2 & 6.3

Section 6.1 Problems 1, 10, 17, 30 & 31

Section 6.2 Problems 1,2,3,6,8, 10 & 11

Section 6.3 Problems 1,2,5,8,20,28,36,41 & 43

.........Due 10-24-2013.............

Assignment

Read Sections 1.3, 8.1, 8.2, 8.3 & 8.5

Section 1.3 Problems 1,6, 7 & 11

Section 8.1 Problems 1, 6, 9 & 22

Section 8.2 Problems 1,3,5,13,14,32 & 33

Section 8.3 Problems 25, 26, 29 & 33

Section 8.5 Problems 1a&b,4,5(hard),7 & 9

Note:the answer to 5 is in book. Try it before you look at answer

............due 11-7-2014......

Assignment

Read Chapter 7

Section 7.1 Problems 1,16,18, 26 & 33

Section 7.2 Problems 1,2,3,15,17,23 & 24

Section 7.3 Problems 1,9,16,17,18,19 & 21

Section 7.4 Problems 3,4,13,22 & 34

Hint on 34: Let S = {s1,s2}. List thye Power Set of S and all possible functions from S to {0,1}

and use what you see as a guide to seeing the way to a formal general proof

......due 11-14-2014............

Assignment

Read Sections 9.1, 9.2, 9.3 & 9.5

Section 9.1 Problems 2,3,5,7,9,18 & 21

Section 9.2 Problems 1,3,6,10,13 & 14

Section 9.3 Problems 1,3 & 12

Section 9.5 Problems 1,2,6 & 8

...........due 12-02-2014............

This is the last assignment for the Homwork Portfolio

and the Homework Portfolio will be collected 12-02-2014

Last Updated 11-20-2014