Name:
CSE 1400
Fall 2015
1
Score
Applied Discrete Mathematics
Practice Quiz 2
Twos complement numbers
(30 pts)
1. What is the decimal value of the twos complement number (00110111)2c ?
2. What is the decimal value of (11000111)2c
3. Negate the twos comple
Page 166
True/False
1.
2.
4.
5.
10.
If a1 = 5 and ak+1 = 3ak for > 1, then a4 = 135 TRUE
If a0 = 5 and ak = 3ak-1 for > 1, then a4 = 135 FALSE
The fourteenth term of the arithmetic sequence with a = 3 and d = 4 is 19 FALSE
The sum of the first four terms
Page 156
True/False
1. The statement ni=1 (2i 1) = n2 for every n N is the type of statement that can be proved by
mathematical induction. True
2. The statement 23n 1 is divisible by 7 for every n N is the type of statement that can be
proved using mathem
Page 190
1a. How many people like at least one of these toppings? 10 + 7 6 = 11
1b. How many people like Canadian bacon but not anchovies? 10 6 = 4
1c. How many people like exactly one of the two toppings? 11 6 = 5
1d. How many like neither? 15 11 = 4
3a.
Page 209
2. Eight horses are entered in a race in which a first, second, and third prize will be awarded. Assuming
no ties, how many different outcomes are possible? 8*7*6 = 336
4. There are 30 people in a class learning about permutations. One after anot
Page 79
1a. f = cfw_(1,1), (2,1), (3,1), (4,1), (3,3) f is not a function because it has two different pairs of (3,#)
1b. f = cfw_(1,2), (2,3), (4,2) f is not a function because there is no form of (3,#)
1d. f = cfw_(1,1), (1,2), (1,3), (1,4) f is not a f
Page 42
1b. cfw_x Z | xy = 15 for some y Z cfw_-15,-5,-3,-1,1,3,5,15
1e. cfw_a | a < -4 and a > 4 cfw_
2d. cfw_n | n + n is a multiple of 3 cfw_2,3,6,8,
9a. List all of the subsets of the set cfw_a, b, c, d that contain
i.
ii.
iii.
iv.
v.
Four elements cf
Mean/1!. 0/05 WEUQQIL
VA% 3
*TTrTZ(IEW
M one M6625 16 be 55
~_AL;7%Z%_.m_
WW
WWW
PAE 8 52:1220559
MW
'16:. TIME
_4_'_
#19. x allege Tam:
R domlufa 2W5
' W515 TELLE
Must) FALSE
T110154 L 4156? I
ob. 11 Is not rm c912. 2+1 0
. A. 455.40 mania/154114,] r
Week 8 Homework
Page: 252
10. Describe an algorithm that, upon input of n real numbers, a1 , a2 ., an , and
another x , determines how many ai are equal to x.
Page: 264
5.
19a.
19c.
19f.
Workbook Page 188:
1. f(n) 25n
25(2n) =2(25n) =2f(n) increased by 2
Name:
CSE 1400
Fall 2015
Applied Discrete Mathematics
Practice Midterm Key
1. Basic counting concepts.
(a) How many bit strings are there of length n?
Answer: There are 2n bit strings of length n.
(b) How many permutations are there on n symbols?
Answer:
Name:
CSE 1400
Fall 2015
Applied Discrete Mathematics
Practice Quiz 3
1. Use mathematical induction to show the sum of the first n natural numbers is the triangular number
tn = n(n 1)/2. (Note the natural numbers start with 0)
2. Show that the function t(
Name:
CSE 1400
Fall 2015
1
Score
Applied Discrete Mathematics
Practice Quiz 2 Key
Twos complement numbers
(30 pts)
1. What is the decimal value of the twos complement number (00110111)2c ?
Answer: (00110111)2c is a positive integer equal to 3 16 + 7 = 55.
Name:
CSE 1400
Fall 2015
Applied Discrete Mathematics
Practice Midterm
1. Basic counting concepts.
(a) How many bit strings are there of length n?
(b) How many permutations are there on n symbols?
(c) How many subsets does an n element set have?
(d) How m
Page 252
10. Describe an algorithm that, upon input of n real numbers, a 1,a2.,an, and another number, x,
determines how many ai are equal to x.
M=0
For I = 1 to n, if ai = x, replace M by M + 1
Output M
Page 264
5. Let x be a real number and n a positive