CHAPTER 3
Counting
t may seem peculiar that a college-level text has a chapter on counting.
At its most basic level, counting is a process of pointing to each object
in a collection and calling o one, two, three,. until the quantity of
objects is determin
MTH 207 Exam 3 F07
LEBANESE AMERICAN UNIVERSITY
DIVISION OF COMPUTER SCIENCE AND MATHEMATICS
MTH 207 DISCRETE STRUCTURES 1
EXAM 3 FALL 2007
Date: January 14, 2008
Time: 75 Minutes
NAME:
ID:
, CHECK THIS BOS ONLY IF YOU WANT YOUR EXAM GARDED BY FRIDAY, JAN
Fig.2; 35539.2 ELEM—6:4
Umgﬁzge On Goa—USE» QOzQw >2: 35523.9
axis m - Eel ~ch can—~55 mazcnecxmm _ I 5:? “a:
6:355? um 2:.
223m" j E
53:96:" UP m. Spawn UP .3. mas—32
Hzﬁmcnjozm” dim $53 nonmmma o», w Ema SE a Eda—mam. Owner Sm: mono mm Emmmim.
>339
MTH 207 Sample Final F2011
LEBANESE AMERICAN UNIVERSITY
DEPARTMENT OF COMPUTER SCIENCE AND MATHEMATICS
SAMPLE QUESTIONS FOR
FALL 2011
FINAL EXAM - MTH 207: DISCRETE STRUCTURES 1
1.
a.
Write the inclusion-exclusion principle for two sets A and B, i.e. com
Spring 2015
MTH207
S. Nahlus
Homework 4
1. There are 18 math majors and 325 CS majors. How many ways are there to pick one
math major and one CS major?
2. How many strings of four decimal digits
a. Do not contain the same digit twice?
b. End with an even
Discrete Mathematics, Spring, 2004 Solutions to Exam 1 You must show all your work. The number of points earned on each problem will be determined by how well you have justified your solution. 1. Use Theorem 1.1.1 to verify the following logical equivalen
D iscrete Math
Discrete Mathematics
Chih-Wei Yi
Dept. of Computer Science
National Chiao Tung University
March 20, 2009
D iscrete Math
Functions
2.3 Functions
2.3 Functions
D iscrete Math
Functions
2.3 Functions
On to section 2.3. . . Functions
From calcu
Placing k books onto n indistinguishable shelves
There are three versions of this problem. For all three it is easier to nd
a solution if we add an extra condition, namely that none of the shelves can
remain empty (each must get at least one book). Once w
Sample Exam I
Discrete Structures I (Hamdan)
Fall 2011
1. If you know that the proposition (p ^ q ) ! r _s is false, what can you say about the truth value of the
propositions
(a) (r_ s s) !s p?
(b) (p) ! q _ r _ s?
2. Write an English statement represent
Denition: Variable and Predicate
Predicates and Quantiers
Discrete Mathematics I MATH/COSC 1056E
Julien Dompierre
Department of Mathematics and Computer Science
Laurentian University
Let the declarative statement:
x is greater than 3.
This declarative sta
CS 3333 Mathematical Foundations
Recitation 8
Practiced on: 3/2
Spring '11
5:30 - 6:20 pm
Permutations and Combinations
Note: These problems are designed for practice during a 50 minute recitation.
a) Easy problems: expected to be solved in 5 min.
b) Medi
Hawk/Eme >ZHEO>Z C2H<HWMHH<
623152: on 033.52. memo—38 a—E guaraiamnm
Ema—68 Earn—swan»: magma—.8 u
EE: ES:— E: 35 €2.55 2. ~38
E
('D
E
O
:3
g
B
O"
(b
*1
0.5%
H. max.
I
E I
I
a. ﬁx.
a. 9x.
q. n
a. «S I
w. ax. I
3. 2x. I
2 ﬁx. I
B. 3. I
8. ex. I
E.
MTH207 Spring2015
S. Nahlus
Homework 5
1. There are 20 people who work in an office together. Four of these people are selected to go to
the same conference together. How many such selections are possible?
a. 80
b. 116280
c. 4845
d. None of the above
2. T
LEBANESE AMERICAN UNIVERSITY
DEPARTMENT OF COMPUTER SCIENCE AND MATHEMATICS
EXAM 3 - MTH 207: DISCRETE STRUCTURES 1 FALL 2011
DURATION: 75 MIN
NAME:
ID:
INSTRUCTOR: DR. S. HABRE
DR. M. HAMDAN
_
INSTRUCTIONS: This exam consists of 8 pages and 7 problems. C
1. Find the gcd d of 20 and 75; then write d as a linear combination of 20 and 75:
2. Consider the equivalence relation on Z
Z given by (m; n)R(p; q) if and only if mq = np:
(a) Find the equivalence class represented by (2; 5):
(b) Describe the set S of t
MTH207 Discrete Mathematics
Summer I 2014
Exam 2
(July 10, 2014)
Name:
ID:
Duration: 60 minutes
Instructor: Silvana Nahlus
Answer the questions in the space provided for each problem.
If more space or scratch is needed, you may use the back pages.
Only sc
MTH207 Discrete Mathematics
Summer I 2014
Exam 3
(July 22, 2014)
Name:
ID:
Duration: 60 minutes
Instructor: Silvana Nahlus
Answer the questions in the space provided for each problem.
If more space or scratch is needed, you may use the back pages.
Only sc
MTH207 Discrete Structures 1
Sample Questions for Exam 1
Fall 2014
1. Let A, B, and C denote three sets.
a. Give an example to show that if A B A C then set B need not equal set C.
b. Give an example to show that if A B A C then set B need not equal set C
MTH207 Discrete Mathematics
Spring 2013-2014
Exam 2
(April 25, 2014)
Name:
ID:
Duration: 60 minutes
Instructor: Silvana Nahlus
Answer the questions in the space provided for each problem.
If more space or scratch is needed, you may use the back pages.
Onl
MTH207 Discrete Mathematics
Spring 2013-2014
Exam 3
(May 23, 2014)
Name:
ID:
Duration: 60 minutes
Instructor: Silvana Nahlus
Answer the questions in the space provided for each problem.
If more space or scratch is needed, you may use the back pages.
Only
MTT207 Spring 2015
S. Nahlus
Class work 3
(Exercises from Previouses)
1. Given that the sets A, B and C are all countable, show that their union is
also countable.
2. Show that A (BUC) = (A B)(A C)
3. If A, B and C are countable sets, show that (AxB)UC is
MTH207
Spring, 2015
th
Discrete Mathematics and its Applications , Rosen 7 ed
Homework I
1.1 Propositional Logic
N9 p13
Let p and q be the propositions
p :You drive over 65 miles per hour.
q :You get a speeding ticket.
Write these propositions using p and
muzsm No:
. m
DA
‘\
p.
N.
kw
w.
P
D
/
Ho.
EAT—Maw m. 2025
0.3.5.203 w
3:03 03 um 30% 32.03 0:0 wmm am 32.03. :02 3m:< 5.35 08 303 H0 3% 0:0
30:. 3&2 0:0 0:0 am 32.01. Fm x mm a I w mmo
10$. 30:0ﬁ13mm 0* 3.05. 0013.1 EEG
0.
JUN (593+ .Tv 9M9? hwwh.fufm§3 €