Math 55: Discrete Mathematics,
UC Berkeley, Fall 2010
Solutions to Homework #1 (due September 8)
September 13, 2010
§
1.1 # 8
a. If you have the flu, then you miss the final examination.
b. You do not miss the final examination, if and only if you pass the course.
c. If you miss the final examination then you do not pass the course.
d. You have the flu or you miss the final examination or you pass the course.
e. If you have the flu then you do not pass the course, or, if you miss the final examination then
you do not pass the course. (Alternatively, if you have the flu or miss the final examinatin
then you do not pass the course.)
f. You have the flu and miss the final examination, or, you do not miss the final examination
and you pass the course.
§
1.1 # 12
A biconditional statement
p
↔
q
is true when
p
and
q
have the same truth values, and is false
otherwise.
a. True
b. False
c. True
d. False
1
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p
q
r
p
→
q
q
→
r
q
∧
r
(
p
→
q
)
∧
(
q
→
r
)
p
→
(
q
∧
r
)
T
T
T
T
T
T
T
T
T
T
F
T
F
F
F
F
T
F
T
F
T
F
F
F
T
F
F
F
F
F
F
F
F
T
T
T
T
T
T
T
F
T
F
T
T
F
T
T
F
F
T
T
T
F
T
T
F
F
F
T
T
F
T
T
Table 1: Truth table for
§
1.2 #22
§
1.1 # 22
a. You get an A in this course if and only if you learn how to solve discrete mathematics
problems.
b. You read the newspaper every day if and only if you will be informed.
c. It rains if and only if it is a weekend day.
d. You can see the wizard if and only if the wizard is not in.
§
1.1 # 24
a. Converse: If I will stay at home, it snows tonight. Contrapositive: If I will not stay at home,
it does not snow tonight. Inverse: If it will not snow today, I will not ski tomorrow.
b. We can restate the given statement as: If it is a sunny summer day, I go to the beach.
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 Fall '08
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 Math, Modus ponens, Modus tollens, universal instantiation

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