Study Guide for Test 3
Math 1165
Spring 2014
Topics
Textbook Sections: 4.5-4.8, 5.1-5.4, 6.1-6.2
Date: April 16
Mathematical Induction / proof questions
Used to prove topics in chapters 4 through 6
examples: 5.1: 29, 32 and 5.2: 7,8
Relations
know wh
Math 1165
November 3, 2005
Test 2
Your name There are 142 points available on this test. You must show all your work. 1. (12 points) Solve the decanting problem for containers of sizes 299 and 279; that is nd integers x and y satisfying 299x + 279y = d wh
Math 1165
April 12, 2007
Test 2
Your name There are 158 points available on this test. You must show all your work. 1. (12 points) Solve the decanting problem for containers of sizes 399 and 379; that is nd integers x and y satisfying 399x + 379y = d wher
Math 1165 Material from Lectures 4 through 6 1. Recurrence Relations
Study Guide for Test 2
(a) Translate among the three denitions of sequence: listing, recursion, closed form. In other words, work problems like number 1 in (newly revised) homework 5. (b
Math 1165
September 22, 2005
Test 1
Your name There are 134 points available on this test. You must show all your work. 1. (20 points) Let P denote the compound proposition defined by P : (p q) r and let Q : p (q r). Test the associativity of by determini
Math 1165
February 22, 2007
Test 1
Your name There are 177 points available on this test. You must show all your work. 1. (20 points) Let P denote the compound proposition dened by P : p (q r) and let Q : (p q) (p r). Test the distributivity of over by de
Math 1165
September 22, 2005
Test 1
Your name There are 134 points available on this test. You must show all your work. 1. (20 points) Let P denote the compound proposition defined by P : (p q) r and let Q : p (q r). Test the associativity of by determini
Math 1165 1. Division Algorithm (DA) (a) Find q and r given a and b.
Study Guide for Test 1
(b) Use DA in algorithms that require repeated division. 2. Arithmetic in other bases (a) Decimals and and representations of integers and fractions. (b) Conversio
Math 1165
February 22, 2007
Test 1
Your name There are 177 points available on this test. You must show all your work. 1. (20 points) Let P denote the compound proposition defined by P : p (q r) and let Q : (p q) (p r). Test the distributivity of over by
Math 1165
November 3, 2005
Test 2
Your name There are 142 points available on this test. You must show all your work. 1. (12 points) Solve the decanting problem for containers of sizes 299 and 279; that is find integers x and y satisfying 299x + 279y = d
Math 1165 December 15, 2005
Discrete Math
Final Exam
Your name It is important that you show your work. The total value of this test is 260 points. 1. (15 points) For each sequence of integers below, determine whether the sequence is the degree sequence f
Math 1165
Study Guide for Final Exam
Material from Lectures 7 through 10. Updated November 24, 2000 The final exam is cumulative. However, it will emphasize material that has been covered since Test 2. 1. Combinatorics (a) Understand and use the addition
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Study Guide for Test 1
Math 1165
Spring 2014
Topics
Textbook Sections: 1.1 - 2.4
Date: February 7
Sets
operations
properties (ie: DeMorgans Laws)
Venn diagrams
Sequences
recursive form
closed (explicit) form
characteristic equation
regular expres
Study Guide for Test 2
Math 1165
Spring 2014
Topics
Textbook Sections: 2.4, 3.1-3.5, 4.1-4.5
Date: March 21
Mathematical Induction
Used to prove topics in chapter 3 & 4
examples: sect 3.5 #36 and sect 4.1 #11
Sequences
recursive and closed (explicit)
Study Guide for the Final Exam
Math 1165
Spring 2014
Format/Topics
Date: April 16
Posets & Lattices (approx. 50%)
Textbook Sections: 6.1-6.4
Posets
definition / order relations
Hasse diagrams
know how to make it from a poset
isomorphic / dual
maxima
Math 1165: Introduction to Discrete Structures
Project Descriptions
Directions and Format
Write a computer program in C/C+ or Java which performs one of the indicated operations
described below. If you would like to write your program in a different progr
Math 1165
May 8, 2007
Final Exam
Your name There are 210 points available on this test. You must show all your work. 1. (20 points) Prove or disprove that and () distributes over implies (). Solution: [(p q) r] [(p r) (q p q r (p q) r) T T T T T T F F T F
Math 1165 December 15, 2005
Discrete Math
Final Exam
Your name It is important that you show your work. The total value of this test is 260 points. 1. (15 points) For each sequence of integers below, determine whether the sequence is the degree sequence f
Math 1165
May 8, 2007
Final Exam
Your name There are 210 points available on this test. You must show all your work. 1. (20 points) Prove or disprove that and () distributes over implies ().
2. (20 points) Suppose you have decanters of sizes 99 and 105. F
Math 1165
April 12, 2007
Test 2
Your name There are 158 points available on this test. You must show all your work. 1. (12 points) Solve the decanting problem for containers of sizes 399 and 379; that is nd integers x and y satisfying 399x + 379y = d wher
Chapter 4.1 Product Sets and Partitions:
> Cartesian Product
0 An ordered pair (a, b) is a listing of objects a and b in a prescribed order, with a
appearing first ad b appearing second.
0 ifA and B are two nonempty sets, we define the product set or Car
Chapter 4.7 Operations on Relations:
)> Operations
0 For a relation R from A to B, (a, b) E R6 iff a is not related to b.
o For a relation R from A to B, (b, a) E R1 iff (a, b) E R.
0 Theorem
I Suppose R and S are relations from A to B:
o IfRESthen R1