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
Week 3 Homework
Kelly Erickson
Discrete Math
Corey Kelly
May 17, 2017
Page 79 Questions 1a, 1b, 1d, 1e, 2a, 2b, 2c, 12, 13, 16a, 16b, 19b.
1a. Not a function; F contains two different pairs of the for
Exercises Pg 252
10: Describe an algorithm that determines how many
o
Step 1: Let E=o
o
Step 2: for
o
i=1 n ,
ai= x Replace E by E+1
If
ai= x
Step 3: Output E
Exercises pgs 264-265
n
5: Algorithms for
Exercises Pgs 190-191
1a: 15 pizza experts, 10 like Canadian bacon let this be C, seven like anchovies let that be A, six
like both
o
( A C)
How many like at least 1?
7+10-6=11
1b: How many like Cana
Exercises pg 209
2: 8 horses 3 positions to be awarded no ties
o
4: 30 students 8leave
o
P ( 8,3 ) =876=336
P (30, 8 ) =3029282726252423=2,359,899,360,000
5: 6 children 3 girls one of whom must ride l
Exercises Pgs 42-43:
cfw_ x Zxy =15 for some y Z
1b:
o
o
cfw_ a N a<4a>4
1e:
o
2d:
Factors of 15
1, 15
3, 5
-1, -15
-3, -5
Therefore cfw_-15, -5, -3, -1, 1, 3, 5, 15
(-, -4) (4, )
cfw_ n N n2 +n
Exercises pgs 78-79:
1a:
f (x ) is not oneto-one
f =cfw_ ( 1, 1 ) , ( 2, 1 ) , ( 3, 1 ) , ( 4, 1 ) ,(3,3)
o
f =cfw_ ( 1, 2 ) , ( 2, 3 ) ,(4, 2)
1b:
o
o
Not a function because for
integer a of (a, b
True/False Pg 166
1: True
o
a1=5
o
a2=15
o
a3 =45
o
a 4=135
2: False
o
a0 =5
o
a1=15
o
a2=45
o
a3 =135
4: False
o
an =a+ ( n1 ) d
o
a 4=3+ ( 41 ) 4
o 3+(3)4
o 3+12
o 15
5: True
n
[2 a+ ( n1 ) d ]
2
o
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)
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: (00
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 nat
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)
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
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MW
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#19. x allege Tam:
R domlufa 2W5
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Must) FALSE
T110154 L 4156? I
ob
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
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
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
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 topp
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 i
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
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
Outpu