WGU C960 DISCRETE MATH II
COMPREHENSIVE EXAM STUDY GUIDE
COMPLETE QUESTIONS AND SOLUTIONS
●● 1.1
Which of these sentences are propositions? What are the truth values of
those that are propositions?
a) Boston is the capital of Massachusetts.
b) Miami is the capital of Florida.
c) 2 + 3 = 5.
d) 5 + 7 = 10.
e) x + 2 = 11.
f ) Answer this question.
Answer: a) Yes, True
b) Yes, False
c) Yes, True
d) Yes, False
e) No
f) No
●● 1.1
,Let p and q be the propositions "Swimming at the New Jersey shore is
allowed" and "Sharks have been spotted near the shore," respectively.
Express each of these compound propositions as an English sentence.
a) ¬q
b) p ∧ q
c) ¬p ∨ q
d) p → ¬q
e) ¬q → p
f) ¬p → ¬q
g) p ↔ ¬q
h) ¬p ∧ (p ∨ ¬q)
Answer: NA
●● 1.1
Let p and q be the propositions
p : It is below freezing.
q : It is snowing.
Write these propositions using p and q and logical connectives
(including negations).
a) It is below freezing and snowing.
b) It is below freezing but not snowing.
c) It is not below freezing and it is not snowing.
d) It is either snowing or below freezing (or both).
,e) If it is below freezing, it is also snowing.
f ) Either it is below freezing or it is snowing, but it is not snowing if it is
below freezing.
g) That it is below freezing.
Answer: NA
●● 1.1
Construct a truth table for each of these compound propositions.
a) p → ¬q
b) ¬p ↔ q
c) (p → q) ∨ (¬p → q)
d) (p → q) ∧ (¬p → q)
e) (p ↔ q) ∨ (¬p ↔ q)
f ) (¬p ↔ ¬q) ↔ (p ↔ q)
Answer: NA
●● 1.2
Translate the given statement into propositional logic using the
propositions provided.
You cannot edit a protected Wikipedia entry unless you are an
administrator. Express your answer in terms of e: "You can edit a
protected Wikipedia entry" and a: "You are an administrator."
, Answer: NA
●● 1.2
Translate the given statement into propositional logic using the
propositions provided.
You can graduate only if you have completed the requirements of your
major and you do not owe money to the university and you do not have
an overdue library book. Express your answer in terms of g: "You can
graduate," m: "You owe money to the university," r: "You have
completed the requirements of your major," and b: "You have an
overdue library book."
Answer: NA
●● 1.2
Express these system specifications using the propositions p "The
message is scanned for viruses" and q "The message was sent from an
unknown system" together with logical connectives (including
negations).
a) "The message is scanned for viruses whenever the message was sent
from an unknown system."
b) "The message was sent from an unknown system but it was not
scanned for viruses."
c) "It is necessary to scan the message for viruses whenever it was sent
from an unknown system."
COMPREHENSIVE EXAM STUDY GUIDE
COMPLETE QUESTIONS AND SOLUTIONS
●● 1.1
Which of these sentences are propositions? What are the truth values of
those that are propositions?
a) Boston is the capital of Massachusetts.
b) Miami is the capital of Florida.
c) 2 + 3 = 5.
d) 5 + 7 = 10.
e) x + 2 = 11.
f ) Answer this question.
Answer: a) Yes, True
b) Yes, False
c) Yes, True
d) Yes, False
e) No
f) No
●● 1.1
,Let p and q be the propositions "Swimming at the New Jersey shore is
allowed" and "Sharks have been spotted near the shore," respectively.
Express each of these compound propositions as an English sentence.
a) ¬q
b) p ∧ q
c) ¬p ∨ q
d) p → ¬q
e) ¬q → p
f) ¬p → ¬q
g) p ↔ ¬q
h) ¬p ∧ (p ∨ ¬q)
Answer: NA
●● 1.1
Let p and q be the propositions
p : It is below freezing.
q : It is snowing.
Write these propositions using p and q and logical connectives
(including negations).
a) It is below freezing and snowing.
b) It is below freezing but not snowing.
c) It is not below freezing and it is not snowing.
d) It is either snowing or below freezing (or both).
,e) If it is below freezing, it is also snowing.
f ) Either it is below freezing or it is snowing, but it is not snowing if it is
below freezing.
g) That it is below freezing.
Answer: NA
●● 1.1
Construct a truth table for each of these compound propositions.
a) p → ¬q
b) ¬p ↔ q
c) (p → q) ∨ (¬p → q)
d) (p → q) ∧ (¬p → q)
e) (p ↔ q) ∨ (¬p ↔ q)
f ) (¬p ↔ ¬q) ↔ (p ↔ q)
Answer: NA
●● 1.2
Translate the given statement into propositional logic using the
propositions provided.
You cannot edit a protected Wikipedia entry unless you are an
administrator. Express your answer in terms of e: "You can edit a
protected Wikipedia entry" and a: "You are an administrator."
, Answer: NA
●● 1.2
Translate the given statement into propositional logic using the
propositions provided.
You can graduate only if you have completed the requirements of your
major and you do not owe money to the university and you do not have
an overdue library book. Express your answer in terms of g: "You can
graduate," m: "You owe money to the university," r: "You have
completed the requirements of your major," and b: "You have an
overdue library book."
Answer: NA
●● 1.2
Express these system specifications using the propositions p "The
message is scanned for viruses" and q "The message was sent from an
unknown system" together with logical connectives (including
negations).
a) "The message is scanned for viruses whenever the message was sent
from an unknown system."
b) "The message was sent from an unknown system but it was not
scanned for viruses."
c) "It is necessary to scan the message for viruses whenever it was sent
from an unknown system."
