JUL2,2009
Venn Diagram - Word Problems
1) Stephen asked 100 coffee drinkers whether they like cream or sugar in their coffee. According to the Venn diagram
below, how many like
a) Cream?
b) Sugar?
c) Sugar but not cream?
d) Cream but not sugar?
e) Cream a
Vim/Linux commands:
Esc- enter command mode
i insert
I first nonblank in the line
:q quit
:q! quit w/out save
:w- save
:wq quit and save
cd + direname change directory
cd go to home dir
mkdir + filename - create a directory
pwd show current dir
Discrete Math: Selected Homework Problems
2006
2.1 Prove: if d is a common divisor of a and b and d is also a linear combination of a and b
then d is a greatest common divisor of a and b. (5 points)
3.1 Prove: if a b (mod m) then gcd(a, m) = gcd(b, m). (5
STUDY PROBLEMS FOR EXAM I
CMSC 203
DISCRETE STRUCTURES
DR. LOMONACO
1. Use the principle of mathematical induction to prove that
n
X
j2 =
n (n + 1) (2n + 1)
,
6
j 2 = 12 = 1 =
1 (1 + 1) (2 1 + 1)
6
P (n) :
j=1
for all integers n 1.
Answer:
Proof (by weak
Discrete Math I Practice Problems for Exam II
The upcoming exam on Thursday, February 9 will cover the material in Sections 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, and 4.1.
Note that this practice exam is NOT synchronized with what you will see on exam day. I wont
Exam in Discrete Mathematics
First Year at The TEK-NAT Faculty
June 11th, 2014, 9.0013.00
ANSWERS
Part I (regular exercises)
Exercise 1 (6%).
Find the expansion of (2x y)4 using The Binomial Theorem.
Answer: 16x4 32x3 y + 24x2 y2 8xy3 + y4
Exercise 2 (8%)
Sample Problems from Discrete Math exams
S Hudson, 4/29/08
Discrete Math (MAD 2104) is not absolutely required to take Combinatorics, but it
would certainly help. If youve passed Multivariable Calculus, the dept deems you smart
enough to catch up on the v
STUDY GUIDE FOR THE FIRST DISCRETE MATH EXAM
1. Combinatorics
Go over combinatorics examples in the text.
Review all the combinatorics problems from homework.
Do at least a couple of extra problems given below.
(1) How many (positive integer) divisors
Guide to Studying Discrete Mathematics
Discrete Mathematics is possibly unlike your previous math classes, so the same practices that got you
through earlier math courses may not be appropriate for this course. In particular, Discrete Mathematics
may be t
Discrete Math Final Exam Topics STUDY GUIDE
Matrix Math
Order m x n (rows by columns)
Square matrix same number of rows and columns
Adding and subtracting must have the same number of rows and columns
Scalar multiplication multiplying a matrix by a number
Discrete Math
1st Six Weeks Project
For this project you will be finding three sets of data on the web or
from a newspaper or magazine. You will need to find raw data, not
just a chart or a table summarizing the data.
1. Find a data set that is categorica
Discrete Mathematics
Test #3
Name:
1. Explain why if seven integers are selected from the first ten positive integers, there must be at least two
pairs of these integers with the sum of eleven.(7pt)
2.
For the following problems the correct answer is give
Predicate Logic
For example, the assertion "x is greater than 1", where x is a variable, is not a proposition
because you can not tell whether it is true or false unless you know the value of x. Thus the
propositional logic can not deal with such sentence
CS49/Math59: Discrete Mathematics
Practice Problems
This is a list of discrete mathematics exercises. Use this to prepare for the pretest to be given the
first week of the semester.
1. Induction. Prove by induction that for any integer n 1, the sum of the
BTech IVth Semester
Paper Code: BTC43
Paper Name: Discrete Mathematics
SYLLABUS
1. Set theory:Notations, representation of a set, different types of set, theorem on subsets
and symmetric difference, Venn diagram, set operation union, intersection
,disjoin
Principle of Mathematical Induction
By: Aashish Srinivas
Introduction to Mathematical Induction
The goal of an inductive proof is to prove that a certain statement, P, is true for a given subset of natural numbers. Given
a statement P, a properly construc
Macroeconomic Theory and Analysys
Homework #4: Production economy and PIH
1
Competitive Equilibrium with Home Production
a) Households Problem The households problem consists on choosing consumption and hours of market labor
in both periods as to maximize