Math 3336 Discrete Mathematics Summer 2014 (Session 4)
Exam 1 Review
On the Math 3336 Exam 1, the student will be expected to:
Sec. Topic
1.1
Determine whether or not a statement is a proposition, and if not, explain why.
Construct Truth Tables
Determine
1. A class has 30 students enrolled. In how many ways can:
(a) four be put in a row for a picture?
(b) all 30 be put in a row for a picture?
(c) all 30 be put in two rows of 15 each (that is, a front row and a back
row) for a picture?
2. Let S = cfw_1, 2,
Content for Test 1
When topics are not mentioned for a section, then it implies everything from
that section will be covered. The exam questions will be similar in nature to
the homework problems given in the class.
Section 1.1
Section 1.2
Translating E
Content for Test 2
When topics are not mentioned for a section, then it implies everything from
that section will be covered. The exam questions will be similar in nature to
the homework problems given in the class.
Section 2.1
Section 2.2
Section 2.3
Name: People Soft
Test 2 Math 3336
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Content for Test 3
When topics are not mentioned for a section, then it implies everything from
that section will be covered. The exam questions will be similar in nature to
the homework problems given in the class.
Section 5.1
Section 5.2
(The last top
September 29, 2015
Name: People Soft
Test 1 l\*Iath 3336
You have 50 minutes to finish the exam. You cannot. use any books or notes.
This test is worth 100 points.
1. 4 pts
Use truth table to show that -1(]) A q) E- ﬁp V —-q.
2. 4 pts
Prove or disprove
Math 3336
Section 10.2
Graph terminology and Special Types of Graphs
Definition: A graph is an object consisting of two sets called its vertex set and its edge set.
The vertex set is a finite nonempty set.
The edge set may be empty, but otherwise its elem
Math 3336
Section 1.1
Propositional Logic
Topics:
Propositions
Connectives
Negation
Conjunction
Disjunction
Implication; contrapositive, inverse, converse
Biconditional
Truth Tables
What is a proposition?
Definition: A proposition is a sentence that is
Homework 05
2.3 2 )
2.3 4 )
2.3 8 )
2.3 14 )
2.3 26
a. Let f : R R be the given function. It is given that f is strictly
increasing, by denition this means that
f (x1 ) < f (x2 ), i x1 < x2 .
(1)
We have to show that f is one to one, this means we have to
Section 10.3
Section Summary
Adjacency Lists
Adjacency Matrices
Incidence Matrices
Isomorphism of Graphs
Representing Graphs:
Adjacency Lists
Definition: An adjacency list can be used to represent
a graph with no multiple edges by specifying the
verti
Math 3336
Section 2.1
Sets
Definition of sets
Describing Sets
Roster Method
Set-Builder Notation
Some Important Sets in Mathematics
Empty Set and Universal Set
Subsets and Set Equality
Cardinality of Sets
Definition: A set is an unordered collection of
Math 3336
Section 1.2
Applications of Propositional Logic
Topics:
Translating English to Propositional Logic
Logic Puzzles
Translating English Sentences
Steps to convert an English sentence to a statement in propositional logic:
1. Identify simple propo
Math 3336
Section 1.4
Predicates and Quantifiers
Topics:
Predicates
Variables
Quantifiers
Universal Quantifier
Existential Quantifier
Negating Quantifiers
De Morgans Laws for Quantifiers
Translating English to Logic
Predicates
Propositional logic
February 19, 2011
Name:
Test 1
Math 3336
You have the full class period to complete the test. You cannot use any books or notes.
This test is worth 250 points.
1. 40 pts.
Prove or disprove whether the formula is a tautology or not:
(a) (p q) (q p)
(b) (p
Math 3336 Discrete Mathematics
Homework #4
Name:_Peoplesoft ID:_
-Instructions:
Submit your homework on time even if incomplete. Late homework, homework through
email, or in person will not be accepted.
Print out this file and use it as a cover sheet.
M
Math 3336 Final Test Review Graph Theory Questions
1. For each graph give an ordered pair description [vertex set and edge set) and an
adjacency matrix, and draw a picture ofthe graph.
a. K6
b. C4
Fill in the blanks.
2.
a. Kn has edges and vertices.
b. Km
KEY Van ms;
Math 3336 Test 1 A Spring 2016
Write your name and UH ID on the cover of the blue book.
You have 50 minutes to nish the exam. You cannot use any books or notes. Please provide
detailed solution for full credit. Clearly mark the answer to each
Homework 03
1.6 2 This is true using modus tollens. The rst statement if p q,
where p is George does not have eight legs and p is George is
not a spider. The second statement is q. THe third is p. We
can therefore conclude that the conclusion of the argum
Homework 01
1.1 2 ( 1 point each)
2
a. Not a proposition, it is a command.
b. Not a proposition, it is a question.
c. It is a proposition, which is false.
d. Not a proposition, since its truth value depends on the
value of x.
e. It is a proposition,
Homework 02
1.4 2 ( 1 point each)
2
a. True
b. False
c. False
d. True
1.4 5 ( 1 point each)
2
a. Some student spends more than ve hours every weekday
in class.
b. All student spend more than ve hours every weekday in
class.
c. Some student does not
Homework 04
1.8 8 ) The number 1 has this property, since the only positive
integer not exceeding 1 is 1 itself, and therefore the sum is 1.
1.8 10 (points 10)
Notice that the two positive integers given are consecutive integers. Let us call n = 2.10500 .
Math 3336
Section 5.1
Mathematical Induction
Mathematical Induction
Examples of Proof by Mathematical Induction
Mistaken Proofs by Mathematical Induction
Guidelines for Proofs by Mathematical Induction
Suppose we have an infinite ladder:
1. We can reach t
Math 3336
Section 1.1
Propositional Logic
Topics:
Propositions
Connectives
Negation
Conjunction
Disjunction
Implication; contrapositive, inverse, converse
Biconditional
Truth Tables
What is a proposition?
Definition: A proposition is a declarative sent
Math 3336
Section 6.1
The Pigeonhole Principle
The Pigeonhole Principle
The Generalized Pigeonhole Principle
The Pigeonhole Principle
If a flock of 20 pigeons roosts in a set of 19 pigeonholes, one of the pigeonholes must have
more than 1 pigeon.
The Pige
Math 3336
Section 2.4
Sequences and Summations
Sequences
Geometric Progression
Arithmetic Progression
Recurrence Relation
Fibonacci Sequence
Summations
Definition: A sequence is a function from a subset of the integers (usually either the set
cfw_0, 1,