CIT 592 - HW8
All deadlines as per canvas
The HW is due as per the deadline posted on Canvas. Please write your answers as
clearly as possible.
Questions
1. Prove by induction that 5n > n! for n 12.
2. Let Fi represent the ith Fibonacci number. Show that

Recitation 3
Recitation Questions.
1. a) How many base 10 numbers have 5 digits.
b) How many 5 digit numbers have no two consecutive digits equal.
c) How many have at least 1 pair of consecutive digits equal.
SOLUTION:
a) 9 10 10 10 10 = 9 104
b) 9 9 9 9

Recitation 3
Recitation Questions.
1. a) How many base 10 numbers have 5 digits.
b) How many 5 digit numbers have no two consecutive digits equal.
c) How many have at least 1 pair of consecutive digits equal.
2. A palindrome is a word that reads the same

Recitation
Recitation Questions.
1. What is R Q? What is Q Z?
2. What is P (P ()?
3. For the sets A, B, C as defined below
A = cfw_1, 2, 5, 8 B = cfw_3, 4, 1, 2, 7 C = cfw_3, 2
what is
A B, A B, A C, C A, A B
4. List the elements of this set explicitly
cf

Recitation 3
Recitation Questions.
1. Provide a combinatorial proof for the following
2n
n
=
n
0
2
n
+
1
2
n
+ .
n
2
n
Hint: Remember that n = nk
k
SOLUTION:
The right part of the equality represents the number of ways we can choose n elements
among 2n el

Recitation 5
Recitation Questions.
1. Let p be the proposition It is below freezing
Let q be the proposition It is snowing
Now express the following statement with logic symbols
It is either below freezing or it is snowing but it is not snowing if it is b

Recitation 4
Recitation Questions.
1. An aircraft emergency locator transmitter (ELT) is a device designed to transmit a
signal in the case of a crash. The Altigauge Manufacturing Company makes 80% of the
ELTs, the Bryant Company makes 15% of them, and th

Recitation 2
Recitation Questions.
1. a) How many base 10 numbers have 5 digits.
b) How many 5 digit numbers have no two consecutive digits equal.
c) How many have at least 1 pair of consecutive digits equal.
SOLUTION:
a) 9 10 10 10 10 = 9 104
b) 9 9 9 9

CIT592
Midterm Exam 1
DO NOT START UNTIL INSTRUCTED TO DO SO.
Answer the questions in the spaces provided on the question sheets.
If you run out of room for an answer, continue on the back of the page.
Each question may or may not be tricky. Please do

Recitation 3
Recitation Questions.
1. Provide a combinatorial proof for the following
( )2
( ) ( )2 ( )2
n
n
n
2n
=
+
+ .
0
1
n
n
2. How many solutions are there to this inequality x1 + x2 + x3 12 where each of the
xi s is non-negative.
3. Suppose a perso

CIT 592 - HW8
All deadlines as per canvas
The HW is due as per the deadline posted on Canvas. Please write your answers as
clearly as possible.
Questions
1. N straight lines divide a plane into several regions. What is the maximum number of
regions that t

CIT592
Midterm Exam 2
You can tear this o and use it as scratch paper. Also, you can use the back
of any sheet as scratch paper.
Algebra
a2 b2 = (a + b)(a b)
a3 b3 = (a b)(a2 + ab + b2 )
a3 + b3 = (a + b)(a2 ab + b2 )
(a b)2 = a2 2ab + b2
Assumed deni

Recitation
Recitation Questions.
1. For the sets A and B as dened below
A = cfw_1, 2, 5, 8 B = cfw_3, 4, 1, 2, 7 C = cfw_3, 2
what is
A B, A B, A C, C A, A B
2. Write the following two sets in set builder form by identifying some property that all
the ele

Recitation 5
Recitation Questions.
1. Prove that the dierence between consecutive perfect squares is odd.
2. Using rst principles show that (B A) (C A) = (B C) A. First principles
means you have to take an arbitrary element in the left side and show it be

Recitation 4
Recitation Questions.
The first few questions are from last week. Let us know which ones you want us to
discuss.
1. a) There are 32 first year MCITs and as part of 591 recitation they are told to randomly pair up and do pair programming. How