Homework 1
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Transcript of Homework 1
Please note that these problems come from the seventh edition of the United States version of Discrete
Mathematics and Its Applications by Kenneth Rosen. The international edition may not contain the same
problems in the same places so be sure that you are using the correct version of the textbook.
Also realize that the odd-numbered problems have answers in the back of the textbook and in most
cases are very similar to the even-numbered problems, so if you are having trouble figuring out a
problem try to work a similar even problem.
Collaboration: While you are allowed to work with other students on these problems, do not give your
solutions or receive solutions from another student. To do so will be considered cheating. Collaboration
means working together as more or less equal partners to find solutions or to double check for similar
conclusions. It is not a free ticket to cheat. Never succumb to pressures from others to hand over your
homework solutions. Again that is cheating - on both accounts - giving and receiving.
Keep in mind any problems that say "show" that something is true, it means to PROVE it, do not simply
give cases that it works for.
Assignment
Section 1.1
2. Which of these are propositions? What are the truth values of those that are propositions?
a) Do not pass go
d) 4 + x = 5
e) The moon is made of green cheese.
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.
Express each of these propositions as an English sentence.
a) ¬p
e) p ↔ q
f) ¬p → ¬q
h) ¬p ∨ (p ∧ q)
18. Determine whether each of these conditional statements is true or false.
b) If 1 + 1 = 3, then dogs can fly.
d) If 2 + 2 = 4, then 1 + 2 = 3.
28. State the converse, contrapositive, and inverse of each of these conditional statements.
a) If it snows tonight, then I will stay at home.
b) I go to the beach whenever it is a sunny summer day.
c) When I stay up late, it is necessary that I sleep until noon.