Question 1
1.5 out of 3 points
Let a graph be specified by the following adjacency matrix:
00001
10000
01000
10001
01100
Select the properties that hold for this graph.
The graph is directed.
Answers: The graph is complete.
The graph is directed.
The gra
Question 1
2 out of 2 points
The following two propositions are logically equivalent:
p (q r)
and
p (r q).
Selected Answer:
True
Answers:
True
False
Response
Feedback:
Correct! The first proposition can be transformed to the second one as follows: p (q
Question 1
1 out of 1 points
If A is a 64 matrix and B is a 45 matrix, then the product AB has 16 entries.
Selected Answer:
Answers:
False
True
False
Response Feedback: Correct! The product is a 65 matrix with 30 elements.
Question 2
2 out of 2 points
Fo
Suppose that a "word" is any string of seven letters of the alphabet, with repeated letters allowed (not case
sensitive). How many words are there?
Selected Answer:
267
Answers:
7
26
267
726
182
Response
Feedback:
For each letter of the word there are 26
Question 1
1 out of 1 points
Let P(n) be the following proposition:
f(n) = f(n-1) + 1 for all n 1, where f(n) is the number of subsets of a set with n elements.
Determine whether P(n) holds.
Selected Answer:
Answers:
False
True
False
Response Feedback: T
Question 1
1 out of 1 points
Determine whether the following rule describes a function with the given domain and codomain:
f : N N where f(n) = n.
Selected Answer:
Answers:
False
True
False
Response Feedback: Correct! The square root operation returns nu
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Review Test Submission: Test 10_
Exams, Assignments & Quizzes
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Review Test Submission: Test 6_
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false
Question 1
0 out of 1 points
A = cfw_4, 8, 9
B = cfw_4, 9
AB
Selected Answer:
Answers:
True
True
False
Question 2
1 out of 1 points
For any two sets A and B, A B = cfw_x | x A x B
Selected Answer:
Answers:
False
True
False
Question 3
2 out of 2 poin
Question 1
1 out of 1 points
The sum of two rational numbers is always irrational.
Selected Answer:
Answers:
False
True
False
Response
Feedback:
The sum of two rational numbers is always rational, which can be proven by a direct
proof (it was studied in
Question 1
1 out of 1 points
A lemma is a helping theorem which can also be thought of as a result needed to prove a main
theorem.
Selected Answer:
Answers:
True
True
False
Response Feedback: Correct!
Question 2
2 out of 2 points
Determine whether the fo
What is the probability that the sum of the numbers on two cubical dice is even when they are rolled?
Selected Answer:
1/2
Answers:
1/36
1/12
1/6
1/4
1/2
Response
Feedback:
Correct! We can list all the possible 36 pairs of numbers and count those whose s
Question 1
2 out of 2 points
The following proposition is a tautology:
(p q) p) q
Selected Answer:
Answers:
False
True
False
Response Feedback: This proposition can be simplified to
p q
which is not a tautology.
Question 2
2 out of 2 points
For all sets
Question 1
1 out of 1 points
Find the number of subsets of the set.
cfw_x | x is a day of the week
Selected Answer:
128
Answers:
127
128
256
124
Response
Feedback:
Correct! The number of subsets of a set is 2n, where n is the cardinality of the set. In
t
Question 1
1 out of 1 points
Translate the given statement into propositional logic using the propositions
provided.
On certain highways in the Washington, DC metro area you are allowed to
travel on high occupancy lanes during rush hour only if there are
Question 1
2 out of 2 points
Two propositions
p (q r)
and
p (q r)
are equivalent.
Selected Answer:
Answers:
False
True
False
Response Feedback: Correct!
Question 2
2 out of 2 points
Two propositions
p (q r)
and
(p q) r
are equivalent.
Selected Answer:
An
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Review Test Submission: Test 11_
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Review Test Submission: Test 9_
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Review Test Submission: Test 5_
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CS381 Discrete Structures Spring 2015
Exam 3 solution
Name: _
(No books or notes are needed, 50 points total)
1. (8 points) True or false.
(a). _F_ 33 mod 7 is 2.
(b). _T_ 1 23
(mod 11).
(c). _F_ If a|bc, then a|b or a|c, where a, b, c are positive intege
CS381 Discrete Structures
Answer to HW2
Section Sets 2.1 (p125-126):
9(c, e, g)
c) False, e) False, g) True
14.
We put the subsets inside the supersets. Thus the answer is as shown.
25.
For the if part, given A B, we want to show that that P(A) P(B), i.e.
CS381 Discrete Structures Spring 2015
Exam 1
Name: _
(No books or notes are needed, total 50 points)
1. ( 12 points) Determine if the following propositions are TRUE or FALSE.
(a). _T_ If 2+2=6 or 1+1 = 2, then 10+2 = 3 or 2+2 = 4.
(b). _F_ 3+1 = 0 if and
Homework 3 solutions
2.3, p.152-155
6) Find the domain and range of these functions.
a) The function that assigns to each pair of positive integers the first integer of the pair. (5 points)
The domain is
and the range is .
d) The function that assigns to
Answers to homework #1 questions:
Question 1 (section 1.1):
10. Show that each of these conditional statements is a tautology by using truth tables.
a) [ p ( p q ) ] q (5 points)
p
T
T
F
F
q
T
F
T
F
p
F
F
T
T
pvq
T
T
T
F
p ^ (p v q)
F
F
T
F
[p ( p q ) ] q
Exam 2 solutions:
1 (a). 17
1 (b). -20
1 (c). 14
2 (a). T
2 (b). F
2 (c). T
2 (d). F
2 (e). F
2 (f). T
2 (g). F
2 (h). T
2 (i). T
2 (j). T
2 (k). F
3.
Remember: A function is a bijection when it is an injection and
also a surjection.
3 (a). It is a biject
CL140103014161
Q 4- Analyze the connections/similarities between William Faulkners stories
Barn Burning (pg 503) and A Rose for Emily (pg 91) in terms of their
psychological setting (the old Souths attachment to past-difficulty in adjusting
to the change)
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Review Test Submission: Test 2_
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