Name:
November 30, 2009
CS 317 Exam II
Instructions: There are six problems in this exam. Some of them consist of several
subproblems. Make sure you look through them carefully. Please write legibly and
justify all your answers.
1. Our goal is to use math
CS 317 Final Exam
May 16, 2016
Instructions: There are eight problems and one bonus problem in this exam Make sure
you look through them carefully and answer all the questions. Please write legibly and
justify all your answers.
1. (5 pts.) Let I(x) be the
CS317 Discrete Information Structures
Fall 2012, TR 11:0011:50pm, EMS E190
http:/www.cs.uwm.edu/classes/cs317
1
Prerequisite
A grade of C or better in Calculus 1 (MATH 221, 226 or 231) and a passing grade in Introductory
Programming (CS152 or CS 201).
2
I
Connectivity in Graphs
Definition 1 In a graph G, a path of length k is a sequence of k + 1 distinct vertices
v0 , v1 , . . . , vk so that cfw_vi , vi+1 is an edge in G for i = 0, . . . , k 1. A cycle of length
k is like a path of length k except its fir
Homework 6
Due 03.27.17 (Monday)
1. The Pigeonhole Principle.
Sec. 6.2: 2, 18
2. Mathematical Induction. Make sure that (i) you determine P (n), the general
statement that youre trying to prove for integer n, (ii) do the basis step and
(iii) do the induct
Coverage for Exam 2
1. Mathematical Induction (Sections 5.1, some of 5.2)
Mathematical induction is a technique for proving statements of the form P (n)
is true for all positive integers n. Every proof by induction consists of two
steps. Know what they ar
Coverage for Exam 2
1. Proof Methods (Section 1.7 and parts of Section 1.8)
We started this section by defining even/odd integers, rational/irrational numbers, prime/composite numbers and the notion of when a divides b. Make sure
you have these definition
Coverage for Exam 2
1. Mathematical Induction (Sections 5.1, some of 5.2)
Mathematical induction is a technique for proving statements of the form P (n)
is true for all positive integers n. Every proof by induction consists of two
steps. Know what they ar
Homework 2
Due 02.13.17 (Monday)
1. Translating English into logical expressions. Sec. 1.5: 10 a to f.
2. Determining the truth values of logical expressions. Sec. 1.5: 26 a to i. Include
an explanation as to why you think the statement is true or false.
Homework 2
Due 09.25.11 (Tuesday)
1. Section 1.4: 38.
2. Section 1.5: 10 (a to f only), 26 (c to i only). Like what we did in class, please
make sure you provide an argument as to why your answer is true or false.
3. Section 1.6: 10 (a, e, f only). For ea
Name:
October 18, 2011
CS 317 Exam I
Instructions: There are six problems in this exam. Some of them consist of several
subproblems. Make sure you look through them carefully. Please write legibly and
justify all your answers.
1. A tautology is a proposit
Name:
March 10, 2009
CS 317 Exam I
Instructions: There are five problems in this exam. Some of them consist of several
subproblems. Make sure you look through them carefully. Please write legibly and
justify all your answers.
1. This question has two part
Name:
November 30, 2009
CS 317 Exam II
Instructions: There are six problems in this exam. Some of them consist of several
subproblems. Make sure you look through them carefully. Please write legibly and
justify all your answers.
1. Our goal is to use math
Coverage for Exam 1
1. Logic (Sections 1.1 - 1.6)
- What is a proposition, a propositional function and the quantifiers that you
can attach to it?
- How are propositions combined to form more complex propositions?
- How do you verify that two compound pro
Name:
October 22, 2013
CS 317 Exam I
Instructions: There are five problems in this exam. Make sure you look through them
carefully. Please write legibly and justify all your answers.
1. (3 pts.) Recall that a tautology is a statement that is always true.
Name:
March 9, 2015
CS 317 Exam I
Instructions: There are five problems in this exam. Make sure you look through them
carefully and answer all the questions. Please write legibly and justify all your answers.
1. (3 pts.) Determine the ? in the statement b
Name:
May 14, 2009
CS 317 Final Exam
Instructions: There are eight questions in this exam, each with multiple subquestions.
Make sure that you read through them carefully, providing as thorough an answer as
you can.
1. (5 pts.) Let P (x), Q(x), R(x) be th
Homework 1
Due 02.06.17 (Monday)
Reminders: It is best that you work early and on your own. You are allowed
to collaborate with your classmates. If you do so, make sure that you write down
their names on the upper right hand corner of the first page of yo
Homework 10
Due 05.03.17 (Wednesday)
1. (Based on Sec. 7.4:10.) Suppose that we flip a fair coin until it comes up tails
twice or we have flipped it six times. Our goal is to determine the expected
number of times we flip the coin.
To do so, we define a r
CS317-401 Discrete Information Structures
Fall 2011, TR 12:0012:50pm, EMS E145
http:/www.cs.uwm.edu/classes/cs317
1
Prerequisite
A grade of C or better in Calculus 1 (MATH 221, 226 or 231) and a passing grade in Introductory
Programming (CS152 or CS 201).
Name:
May 11, 2015
CS 317 Finals
Instructions: There are eight problems and a bonus question in this exam. Make sure
you look through them carefully and answer all the questions. Please write legibly and
justify all your answers.
1. (6 pts.) Let P (m, n)
Coverage for Exam 2
1. Proof Methods (Section 1.7 and parts of Section 1.8, Section 6.2)
We started this section by defining even/odd integers, rational/irrational numbers, prime/composite numbers and the notion of when a divides b. Make sure
you have the
A simple rule for checking when a number is divisible by 3
Let x be an integer. What is a quick way to determine of x is divisible by 2 or 5?
Heres a simple rule for determining if x is divisible by 3: an integer x is divisible by
3 if and only if the sum
CS317 Discrete Information Structures
Spring 2017, MW 1:001:50pm, PHY 135
http:/www.cs.uwm.edu/classes/cs317
1
Prerequisite
Math Placement A; grade of C or better in CS 250.
2
Instructor Info
Instructor: Christine Cheng, EMS 1011, 229-5170, [email protected]
Homework 3
Due 02.20.17 (Monday)
1. Applying rules of inference. Remember that if you see statements that involve
the for all or there exists quantifier, you also have to make use of the rules
of inference for quantified statements (e.g. universal instant
CS317 Discrete Information Structures
Fall 2013, TR 11:0011:50pm, EMS E145
http:/www.cs.uwm.edu/classes/cs317
1
Prerequisite
A grade of C or better in Calculus 1 (MATH 221, 226 or 231) and a passing grade in Introductory
Programming (CS152 or CS 201).
2
I
Name:
October 23, 2012
CS 317 Exam I
Instructions: There are five problems in this exam. Make sure you look through them
carefully. Please write legibly and justify all your answers.
1. (4pts.) This problem is about the proposition p (q r).
a. Using propo
Coverage for Exam 1
1. Logic (Sections 1.1 - 1.6)
- What is a proposition, a propositional function and the quantifiers that you
can attach to it?
- How are propositions combined to form more complex ones?
- How do you verify that two compound proposition
Homework 9
Due 04.17.17 (Monday)
1. A bag contains thirty marbles numbered from 1 to 30. Five marbles are drawn
at random from the bag. There are a few ways to think about this:
a. Marbles are drawn one at a time without replacement. That is, once a marbl
Basic Bayes Theorem
Suppose E and F are events from a sample space S such that p(E) > 0 and p(F ) > 0. Since
E F and E F are disjoint and E = (E F ) (E F ), we have
p(E) = p(E F ) + p(E F ).
If conditional probabilities are known, we can use them to deter