JesseJoseph
ProfessorSuciu
CMSC150
1. Enumeratetheelementsofthefollowingsets:
a. cfw_x:xisanoddpositiveintegerlessthan13
b. cfw_y:yisapositiveintegerthatisamultipleof4andgreaterthan10butlessthan
25
Solution:
a. x=cfw_1,3,5,7,9,11
b. y=cfw_12,16,20,24
2. W
CMSC 150
Homework 2
1. Translate the following English sentences into statements of predicate
calculus.
A) All programmers enjoy discrete mathematics.
Px= x is programmer
Py= y is enjoy discrete mathematics
( x)( Px Py )
B) Some integers are not odd.
Ix=
1.
Enumerate the elements of the following relations from the set A of positive integers less then
or equal to 10 to the set B of positive integers less then or equal to 30.
A= cfw_1, 2, 3, 4, 5, 6, 7, 8, 9, 10
B= cfw_1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Lab 6 Data Element Class
Lab Objectives

Be able to declare a new class
Be able to write a constructor
Be able to write instance methods that return a value
Be able to write instance methods that take arguments
Be able to instantiate an object
Be able to
1.
Enumerate the elements of the following relations from the set A of positive integers
less than or equal to 10 to the set B of positive integers less than or equal to 30.
1. An element a of A is related to the element b of B if b = 3 a
cfw_(1,3), (2, 6
1. Translate the following English sentences into statements of predicate calculus.
a. All programmers enjoy discrete mathematics
X = programmer
E(x) = Enjoys discrete mathematics
(x)E(x)
b. Some integers are not odd
X = integers
N(x) = x is not odd
(x)N(
1.
Enumerate the elements of the following sets:
1. cfw_x: x is an odd positive integer less than 13
cfw_1,3,5,7,9,11
2. cfw_y: y is a positive integer that is a multiple of 4 and greater than 10 but
less than 25
cfw_12,16,20,24
2.
What is the cardinality
CMIS 150
Homework 4
1. Enumerate the elements of the following sets:
a. cfw_x: x is an odd positive integer less than 13
cfw_1, 3, 5, 7, 9, 11
b. cfw_y: y is a positive integer that is a multiple of 4 and greater than 10 but less
than 25
cfw_12, 16, 20, 2
CMSC 150
Homework 1
1. Whichofthefollowingsentencesarelogicalstatements?
a.
Ifxevendividesy,thenxisafactorofy
b.
IfJohndoeswellindiscretemath,thenhewillbeanexcellentprogrammer
c.
2istheonlyevenprimenumber
d.
Heisthebeststudentintheclass
2. Constructthetru
CMSC 150 Section 6380 Spring 2017 Assignment 4 Answer Sheet
Name:
1: Enumerate the elements of the following sets:
a. cfw_x: x is an odd positive integer less than 13
cfw_1, 3, 5, 7, 11
b. cfw_y: y is a positive integer that is a multiple of 4 and greater
This homework received 100% from professor
CMSC 150 Section 6380 Spring 2017 Assignment 4 Answer Sheet
Name:
1: Enumerate the elements of the following sets:
a. cfw_x: x is an odd positive integer less than 13
Let A = cfw_x: x is an odd positive integer l
Corrected answers are in red
CMSC 150 Section 6380 Spring 2017 Assignment 5 Answer Sheet
Name:
1: Enumerate the elements of the following relations from the set A of positive integers less than
or equal to 10 to the set B of positive integers less than or
Corrected answers are in red
CMSC 150 Section 6380 Spring 2017 Final Exam Answer Sheet
Name:
1: For each the following groups of sets, determine whether they form a partition for the set of
integers. Explain your answer.
a.
A1 = cfw_n Z : n > 0
A2 = cfw_n
This homework received 100% from the professor
CMSC 150 Section 6380 Spring 2017 Assignment 7 Answer Sheet
Name:
1: Calculate the number of integers divisible by 4 between 50 and 500, inclusive.
N = 4k
500 = 52 + 4(n1)
4(n1) = 500  52 = 448
n  1 = 448
This homework received 100% from the professor
CMSC 150 Section 6380 Spring 2017 Assignment 3 Answer Sheet
Name:
1: Prove that the difference of two odd integers is even. Give a justification
at each step.
Let x and y be odd integers and
( ( x ) ) ( ( y )
This homework received 100% from the professor
CMSC 150 Section 6380 Spring 2017 Assignment 6 Answer Sheet
Name:
1: Determine whether each of the following functions is 1to1 and whether it is onto. Assume
the domain and codomain is Z, the integers. Exp
Corrected answers in red
CMSC 150 Section 6380 Spring 2017 Assignment 2 Answer Sheet
Name:
1: Translate the following English sentences into statements of predicate calculus.
a. All programmers enjoy discrete mathematics.
( x)( P( x ) P ( y)
where P(x) =
Corrected answers are in red
CMSC 150 Section 6380 Spring 2017 Assignment 1 Answer Sheet
Name:
1: Which of the following sentences are logical statements?
a: If x even divides y, then x is a factor of y
This is a Logical statement not logical
b: If John d
CMSC 150
Homework 3
1. Prove that the difference of two odd integers is even. Give a justification at
each step
Let q and r be odd integers, ( ( q ) ) ( ( r ) ) [O ( q ) O ( r ) E ( qr ) ]
Statement
O(q)
Justification
O(r)
O(q)
q= 2k+1
O(r)
r= 2k+1
q r=
Homework #1
1. B & C
2. p
T
T
F
F
q
T
F
T
F
~p
F
F
T
T
p ^ ~p
F
F
F
F
(p ^ ~p) ^ q
F
F
F
F
Contradiction everything returned false
p
T
T
F
F
q
T
F
T
F
~p
T
F
T
T
(p V q) (q V p)
T
F
T
F
Neither False and True returns
p
T
T
T
T
F
F
F
F
q
T
T
F
F
T
T
F
F
r
1. Enumerate the elements of the following sets:
a. cfw_x: x is an odd positive integer less than 13
cfw_1, 3, 5, 7, 9, 11
b. cfw_y: y is a positive integer that is a multiple of 4 and greater than 10 but less
than 25
cfw_12, 16, 20, 24
2. What is the car
1. (10 pts) For each the following groups of sets, determine whether they form a
partition for the set of integers. Explain your answer.
a. A1 = (n Z : n > )
A 2 = ( n Z : n < 0)
Al = contain all the integers greater than 0
A2 = contain all the integers l
1. Calculate the number of integers divisible by 4 between 50 and 500, inclusive.
( ( 500 52 ) / 4 ) + 1 = ( 448 / 4 ) + 1 = 112 + 1 = 113
2. Hexadecimal digits are formed using either a numeric decimal digit or a letter
from A to F. How many possible dig
1. Prove that the difference of two odd integers is even. Give a justification at
each step
Let q and r be odd integers, ( ( q ) ) ( ( r ) ) [O ( q ) O ( r ) E ( qr ) ]
Statement
O(q)
Justification
O(r)
O(q)
q= 2k+1
O(r)
r= 2k+1
q r= (2k+1)
= 2n2m
= 2(n
1.
Prove that the difference of two odd integers is even. Give a justification at each
step.
2.
(x) Z, [D(O(x1),O(x2) E]
(hyp) the initial argument.
D(x,y)
O(x)
E
Z
For all odd integers x, y: x y = n, n is an
even integer
x = 2k1+1
y = 2k2+1
(2k1+1)(2k2+
Lecture Notes in Discrete Mathematics
Marcel B. Finan
Arkansas Tech University
c
All
Rights Reserved
2
Preface
This book is designed for a one semester course in discrete mathematics
for sophomore or junior level students. The text covers the mathematical
1.
2.
Determine whether each of the following functions is 1to1 and whether it is onto.
Assume the domain and codomain is Z, the integers. Explain your answers.
a. f(n) = n / 2, assuming integer division
This function is onetoone. There are no two or
David McCarty
CMSC 150
1.
Calculate the number of integers divisible by 4 between 50 and 500, inclusive.
Just divide the numbers by 4 and cut out any remainder. E.g.
50
=12 < the
4
number of integers between 0 and 50 divisible by 4. There are 12 integer
CMSC 150 Section 6380 Spring 2017 Assignment 1 Answer Sheet
Name:
1: Which of the following sentences are logical statements?
a: If x even divides y, then x is a factor of y
b: If John does well in discrete math, then he will be an excellent programmer
c: