Islamic University of Gaza
Computer Engineering Department
Discrete Mathematics
Chapter One
Section 1.1
2. Which of these are propositions? What are the truth values of those that are propositions?
a) Do not pass go.
This is not a proposition; it's a command.
b) What time is it?
This is not a proposition; it's a question.
c) There are no black flies in Maine.
This is a proposition that is false.
d) 4 + x = 5.
This is not a proposition; its truth value depends on the value of x.
e) The moon is made of green cheese.
This is a proposition that is false.
f) 2^n ≥ 100.
This is not a proposition; its truth value depends on the value of n.
4. What is the negation of each of these propositions?
a) Jennifer and Teja are friends.
Jennifer and Teja are not friends.
d) 121 is a perfect square.
121 is not a perfect square.
8. Let p and q be the propositions
p : I bought a lottery ticket this week.
q : I won the million dollar jackpot on Friday.
Expression each of these propositions as an English sentence.
d) p˄q
I bought a lottery ticket this week and I I won the million dollar jackpot.
e) p ↔ q
I bought a lottery ticket this week if and only if I won the million dollar jackpot on Friday.
Chapter One
Section 1.1
f) ¬p → ¬q
If I did not buy a lottery ticket this week, then I did not win the million dollar jackpot on Friday.
g) ¬p˄¬q
I did not buy a lottery ticket this week and I did not win the million dollar jackpot.
12. Let p, q and r be the propositions
p: You have the flu.
q: You miss the final examination.
r: You pass the course.
Express each of these propositions as an English sentence.
c) q →¬r
If you miss the final examination, then you will not pass the course.
d) p˅q˅r
You have the flu orr you miss the final examination or you pass the course.
14. Let p, q and r be the propositions
p: You get an A on the final exam.
q: You do every exercise in this book.
r: You get an A in this class.
Write these propositions using p, q and r and logical connectives (including negations).
a) You get an A in this class, but you do not do every exercise in this book.
p∧¬q
b) You get an A on the final, you do every exercise in this book, and you get an A in this
class.
p∧q∧r
30. How many rows appear in a truth table for each of these compound propositions?
To find the number of rows of the truth table use the following equation where:
n = number of propositions:
2n = number of rows
2
Chapter One
Section 1.1
a) (q → ¬p) ∨ (¬p → ¬q)
n=2
22 = 4
4 rows
b) (p ∨ ¬t) ∧ (p ∨ ¬s)
n=3
23 = 8
8 rows
c) (p → r) ∨(¬s → ¬t) ∨ (¬u → v)
n=6
26 = 64
64 rows
d) (p ∧ r ∧ s) ∨ (q ∧ t) ∨ (r ∧ ¬t)
n=5
25 = 32
32 rows
34)
Construct a truth table for each of these compound propositions.
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