CSE 1400 Applied Discrete Mathematics
Logic & Sets
Department of Computer Sciences
College of Engineering
Florida Tech
Spring 2012
Problems on Boolean Logic
1. (Student will be able to identify the symbols used in Boolean logic.) Match the term with its s
Name:
CSE 1400
Fall 2012
1
Applied Discrete Mathematics
Sample Final Exam
Boolean Logic
1. Which of the following are True and which are False?
(a) p q p.
(b) (p q) (p q).
(c) (p q) (p q).
(d) (p q p) (p p).
2. How many dierent truth assignments can be ma
CSE 1400 Applied Discrete Mathematics
Relations and Functions
Department of Computer Sciences
College of Engineering
Florida Tech
Spring 2012
Problems labeled
!
are important and must be
mastered.
Problems on Relations
Background
A (binary) relation is a
CSE 1400 Applied Discrete Mathematics
Number Theory and Proofs
Department of Computer Sciences
College of Engineering
Florida Tech
Spring 2012
Problems labeled
!
are important and must be
mastered.
Problems for Number Theory
Background
Number theory is th
CSE 1400 Applied Discrete Mathematics
Naming and Number Systems
Department of Computer Sciences
College of Engineering
Florida Tech
Spring 2012
Problems labeled
!
are important and must be
mastered.
Problems on Naming Systems
Background
Names are made fro
CSE 1400 Applied Discrete Mathematics
Sequences, Induction & Recursion
Department of Computer Sciences
College of Engineering
Florida Tech
Spring 2012
Problems labeled
!
are important and must be
mastered.
Problems on Sequence
Background
Sequences are obj
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Quiz Two
1. (15 pts) Let M and L denote the sets of mathematicians and logicians, respectively, and let loves(m, l)
denote the predicate m loves l. Write the two statements below as English sente
D E PA R T M E N T O F C O M P U T E R S C I E N C E S
COLLEGE OF ENGINEERING
FLORIDA TECH
DISCRETE
M AT H E M AT I C S
HOMEWORK
WILLIAM SHOAFF
FA L L 2 0 1 3
Problems Sets
5
Overview
7
Logic
Sets
11
Sequences
13
Recursion
15
19
Summations
Induction
21
Re
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Quiz Six
1. (5 pts) Let (1 001 1001)f p be a normalized oating point number with a sign bit, a 3 bit exponent
written as a biased number with bias b = 4, and a 4 bit fraction. What is the decimal
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Midterm Exam
1. (5 pts) How many truth assignments are there on n Boolean variables?
Answer: There are 2n truth assignments.
Score
2. (5 pts) How many Boolean functions on n Boolean variables are
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Quiz Six
1. (5 pts) Let (0 110 1101)f p be a normalized oating point number with a sign bit, a 3 bit exponent
written as a biased number with bias b = 4, and a 4 bit fraction. What is the decimal
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Quiz Two
1. (15 pts) Let C and PR denote the sets of candidates in political races and let wins(c, r) denote
the predicate candidate c wins race r. Write the two statements below as English sente
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Quiz Three
1. (15 pts) Consider the sequence of partial sums of the rst n natural numbers
n1
k = 0 + 1 + 2 + 3 + + (n 1) with initial condition s0 = 0
sn =
k=0
(a) What are the rst 7 terms in the
Theoretical Computer Science Cheat Sheet
Denitions
Series
i positive c, n0 such that
0 f (n) cg(n) n n0 .
f (n) = O(g(n)
n
i=1
i positive c, n0 such that
f (n) cg(n) 0 n n0 .
f (n) = (g(n)
f (n) = (g(n)
n
im =
1
m+1
i=1
n
greatest b R such that b
s, s S.
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Quiz Five
1. (10 pts) Unicode is a standard for encoding text characters used in most of the worlds writing systems.
There are 109, 976 (printable) characters in Unicode (version 6.2).
(a) How ma
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Quiz Five
1. (10 pts) The native character encoding of the Java programming language is UTF-16: A Java character
is encoded as a 16 bit string.
(a) How many dierent Java characters strings of len
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Quiz One
1. (5 pts) What mathematical symbols are used to express the following Boolean operations?
(a) or
(b) and
(e) implies
(c) not
Score
(d) exclusive xor
(f) equivalent
2. (5 pts) How
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Quiz One
1. (5 pts) What English words are used to express the following Boolean operations?
(a) and
(b) or
(e) exclusive xor
(c) not
Score
(d) implies
(f) equivalent
2. (5 pts) How many truth as
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Quiz Four
1. (30 pts) Let a and b be integers and let n be a positive integer. Consider the relation a is congruent
to b mod n, written a b (mod n), and meaning (c Z)(a b = nc).
(a) Is congruence
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Quiz Three
1. (15 pts) Consider the sequence of partial sums of the rst n powers of 2.
n1
2k = 1 + 2 + 4 + 8 + + 2n1
sn =
with initial condition s0 = 0
k=0
(a) What are the rst 7 terms in the seq
Name:
CSE 1400
Fall 2012
Score
Applied Discrete Mathematics
Quiz Four
1. (30 pts) Let a and b be natural numbers. Consider the relation a divides b, written a | b, and
meaning (c N)(ac = b).
(a) Is divides reexive? Explain your answer.
Answer: Yes, divide