CS 173: Discrete Structures, Fall 2009
Quiz 1 Review problems
Here are some short answer problems that will be helpful in preparing for the first quiz.
Please do them and then check your answers against the posted solutions. You do not need
to hand these in for us to grade.
1. Primes
(a) Express the numbers 350, 105, and 64 as products of primes.
Solution:
350 = 2
·
5
2
·
7, 105 = 3
·
5
·
7, and 64 = 2
6
(b) Compute GCD(350
,
105), GCD(105
,
64), and LCM(350
,
64). Feel free to give large
results as products of primes; multiplying them out is not necessary.
Solution:
GCD
(350
,
105) = 5
·
7
GCD
(105
,
64) = 1
LCM
(350
,
64) = 2
6
·
5
2
·
7
(c) According to the definitions given in the book (or in lecture 7), which integers are
neither prime nor composite?
Solution:
All integers which are strictly less than 2.
2. Divisibility, congruence mod k
Which of the following statements are correct? Show work or give brief explanations
for your answers.
Solution:
(a)
−
6

30 is correct because 30 = (
−
6)
·
(
−
5).
(b) 30
 −
6 is incorrect because
∄
k
∈
Z
such that
−
6 = 30
·
k
.
(c) 6
 −
30 is correct because
−
30 = 6
·
(
−
5).
(d)
−
18

0 is correct because 0 =
−
18
·
0. Zero is a multiple of any integer.
(e) 0
 −
18 is incorrect because 0
n
is always 0, not 18.
3. Miscellaneous questions
(a) When is
⌊
x
⌋
equal to
⌈
x
⌉
?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Erickson
 Evenness of zero, i=0

Click to edit the document details