Lecture Notes on Discrete Structures
Eleftherios Gkioulekas
Copyright c 2014 Eleftherios Gkioulekas. All rights reserved.
Permission is granted to make and distribute verbatim copies of this document, only on a
strictly non-commercial basis, provided the
Question 1:
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
true
unknown
unknown
true
true
unknown
true
unknown
unknown
true
Question 2:
a)
b)
c)
d)
e)
f)
true
true
false. For example: X = , Y = , Z = cfw_1 leads to = cfw_1. Contradiction!
true
true
true
Question 3:
a) 500
CS/MATH320L - Applied Discrete Math Spring 2013
Instructor: Marc Pomplun
Practice Midterm Exam
Duration: 75 minutes
Question 1: _ out of _ points
Question 2: _ out of _ points
Question 3: _ out of _ points
Question 4: _ out of _ points
Question 5: _ out o
CS 320L Applied Discrete Mathematics Spring 2015
Instructor: Marc Pomplun
Assignment #4
Sample Solutions
Question 1: Family Issues
Mary has two kids, Elena and Frank. Elena has a daughter named Jessica, and Frank is
the father of Christine and John.
a) Wr
CS 320L Applied Discrete Mathematics Spring 2015
Instructor: Marc Pomplun
Assignment #3 Sample Solutions
Question 1: On Pigeons and Pigeonholes
Professor P. has an odd habit: He only buys red, green, and blue books, and he keeps
them in completely unorder
CS 320L Applied Discrete Mathematics Spring 2015
Instructor: Marc Pomplun
Assignment #2
Sample Solutions
Question 1: Hilarious Numbers
Let us define that a positive integer is called hilarious if it has exactly three unique prime
factors. For example, 30
CS 320L Applied Discrete Mathematics Spring 2015
Instructor: Marc Pomplun
Assignment #1 Sample Solutions
Question 1: Hair Splitting with Set Expressions
Let us define the successor of the set A to be the set A cfw_A. Find the successors of the
following s
, 8mg ,GMH, THEQKY
fwmu §
.' AMaL {vafh is M (Jami Jdnof égmf>{s
V. a) A, Sat 0? \IQVhCCS VG?) ,
Q) A set 92 .echbcs EU?) , s
GWVA <L<b, Ce HG) .Jco <1 uucque, yoliv 0? V¥£i<e>
Comm EV(£>)V><V(b)., , ._ .
. M)GI._Ladlme.,resen£91:i9h_;
Practice Exam Solutions
Question 1:
a) 4
b) 1
c) 0
d) 2
e) 3
f) 4
g) 5
h) 4
i) 1
j) 2
Question 2:
a) Yes.
b) Yes.
c) No, it is not transitive. a and b could have the same father, and b and c could have the
same mother, without a and c sharing a common par