MA2201/082022 Discrete Mathematics
Eractice Test
1. Write the negation of the statement, She is neither rich nor famous.
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"2. Let enot
MA2201/C82022 Discrete Mathematics NAME: 50? "
Test 2A Take home, Due Friday, February 17, 2017
You may use any resources, but show as much work as possible. Indicate which resources you have used,
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Practice Test 3 SW D 06) 2&4 0X 2 @4 0X: a
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1. Let r) m x. Use Ma
Discrete Math Hw 5
21
Give an explicit formula for a function from the set of integers to the set of positive integers that is
(a) one-to-one, but not onto.
(
f (x) =
4x
x<0
4x + 2 x 0
(b) onto, but n
SWITCHING CIRCUITS
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Current canow through a closed circuit.
Current cannot ow through an open circuit.
Circuit diagrams:
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cfw_flany switch is open current will not ow.
MA2201/CS2022: DISCRETE MATHEMATICS TERM C17
Instructor:
Professor Peter R. Christopher
email: [email protected]
Telephone: 508-831-5269
Office: SH 305B
Office Hours: Monday: 1:00pm-2:00pm
Tuesday: 2:00
MA2201/CS2022 Discrete Mathematics
Practice Test 3
1. Let f (x) = xn . Use Mathematical Induction (and properties of derivatives) to prove f (x) = nxn1 .
2. How many dierent rooms are needed to schedu
MA2201/CS2022 Discrete Mathematics
Practice Test
1. Write the negation of the statement, She is neither rich nor famous.
2. Let p, q, r denote the following statements:
p: I stayed up late,
q: I am ti
CS2022/MA2201
HW#9
DUE: Thursday, October 14
1. (2 points) Which of the following are partitions of cfw_1,2,3,.,10
(a) cfw_2,4,6,8, cfw_1,3,5,9, cfw_7,10
(b) cfw_1,2,4,8,cfw_2,5,7,10,cfw_3,6,9
(c) cfw
CS2022/MA2201
HW#8 SOLUTIONS
1) (a) C ( n,0) p 0 (1 - p )
n- 0
n
(b)
C ( n, k ) p (1 - p)
n- k
k
= (1 - p )
n
. Since this event is the complement of the event of having
k =1
exactly 0 successes, its
CS2022/MA2201
HW#8 SOLUTIONS
1. a This is an equivalence relation.
b This is an equivalence relation.
c This is not an equivalence relation since it is not transitive.
d This is not an equivalence rel
CS2022/MA2201
HW#8
DUE: Friday, October 8
1. (8 points) Do Exercise 4.5.26 from our text.
2. (3 points) Do Exercise 4.5.32 from our text.
3. (14 points) Determine whether each of the following binary
CS2022/MA2201
HW#8
DUE: Monday, April 30
1. (8 points) Adapted from Rosen. Consider the following relations:
R1 = cfw_( x, y ) 2 | x > y
R2 = cfw_( x, y )
R3 = cfw_( x, y )
R4 = cfw_( x, y )
R5 = c
CS2022/MA2201
HW#8
DUE: Tuesday, October 14 (Covers graphs.)
1. (8 points) For which values of n are these graphs bipartite?
(a) Kn
(b) Cn
(c) Wn
(d) Qn
(Note that this is Exercise 8.2-24 of our text.
CS2022/MA2201
HW#7 SOLUTIONS
1) (a) 1/64 (b) 3/64 (c) 1/8.
2) The probabilities of the three outcomes are not equal. The probability that both are
heads is .
3) (a) 10/105 (b) 95/105.
4. (a) 15/40
(b)
CS2022/MA2201
HW#8
DUE: Tuesday, October 16
1. (5 points) Do Exercise 6.5.2 (the second Exercise on pg. 413) of our text.
2. (3 points) Do Exercise 6.5.12 of our text.
3. (12 points) A graph is a cubi
CS2022/MA2201
HW#7 SOLUTIONS
1. The CONJECTURE is true. If R and S are reflexive, then
cfw_a, a | a A R and
cfw_a, a | a A S . Therefore, cfw_a, a | a A R S , so R S
2. The CONJECTURE is true. If R is
CS2022/MA2201
HW#7
DUE: Monday, October 4
1. (3 points) Suppose you and a friend each choose at random an integer between 1 and 8.
For example, some possibilities are (3,7), (7,3), (4,4), (8,1), where
CS2022/MA2201
HW#7
DUE: Monday, April 23
1. (3 points) Assume that there are 65 students in our class, and I draw 3 people
randomly. Also assume that none of them were born in a leap year. What is the
CS2022/MA2201
HW#7
DUE: Thursday, October 11
1. (4 points) Prove or give a counterexample to the following:
CONJECTURE: For any set A and any binary relations R and S on A, if R and S are
reflexive, t
CS2022/MA2201
HW#6 SOLUTIONS
1. There are 410 possible answer sheets, so 2*410+1 students in the class would assure that
at least three people had the same answer sheet.
2. a Let Ek , 1 k 100 , denote
CS2022/MA2201
HW#6 SOLUTIONS
1. If n=0, then there are no strings. If n=1, then there is one string, namely 1. If n 2 ,
then there are n-2 choices for the intermediate bits. Hence, the number of strin
CS2022/MA2201
HW#6
DUE: Tuesday, September 28
1. (2 points) Do Exercise 4.1.14 from our text.
2. (2 points) You are drawing n cards from a playing deck of 52 cards. What is the
minimum value of n to a
CS2022/MA2201
HW#6
DUE: Monday, April 16
1. (8 points) Consider the set of all functions f : cfw_1,., n cfw_0,1 where n
+
.
a How many such functions are there?
b How many such one-to-one functions a
CS2022/MA2201
HW#6
DUE: Friday, October 3 (Covers material through the end of Chapter 5.)
For these problems, you neednt evaluate binomial coefficients. That is, you may leave terms
like C ( 852,255 )
CS 2022/ MA 2201 Discrete Mathematics
A term 2014
Solutions for Homework 5
1. Prove the combinatorial identity
n
r
r
n
=
k
k
nk
,
rk
whenever n, r and k are positive integers with r n and k r,
(a) usi
CS2022/MA2201
HW#6
DUE: Friday, October 5
1. (3 points) A professor teaching a Discrete Math course gives a multiple choice quiz
that has 10 questions, each with 4 possible responses: a, b, c, d. What