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EECS 203: DISCRETE MATHEMATICS
Homework 1 Solutions
1.1.10
a.
r
∧¬
q
b.
p
∧
q
∧
r
c.
r
→
p
d.
p
∧¬
q
∧
r
e. (
p
∧
q
)
→
r
f.
r
↔
(
q
∨
p
) (this English sentence could also be translated as
r
↔
(
q
⊕
p
).)
1.1.14
a. True. Since “1 + 1 = 3” is false, the implication “1 + 1 = 3”
→
“unicorns exist” is true regardless
of whether unicorns exist.
b. True. Same reason as
a
.
c. False. The implication “1 + 1 = 2”
→
“dogs can ﬂy” is true except when “1+1=2” is true (which
it is) and “dogs can ﬂy” is false (which it is.)
d. True. Both 2 + 2 = 4 and 1 + 2 = 3 are true.
1.1.26 (a) 4. There are two atomic propositions (
p
and
q
) and two possibilities for each (T and F).
(b) 8. Three atomic propositions, 2
3
= 8.
(c) 64 = 2
6
.
(d) 32 = 2
5
.
1.1.28
p
q
p
→ ¬
p
p
↔ ¬
p
p
⊕
(
p
∨
q
)
(
p
∧
q
)
→
(
p
∨
q
)
(
q
→ ¬
p
)
↔
(
p
↔
q
)
(
p
↔
q
)
⊕
(
p
↔ ¬
q
)
T
T
F
F
F
T
F
T
T
F
F
F
F
T
F
T
F
T
T
F
T
T
F
T
F
F
T
F
F
T
T
T
1.2.12
a.
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 Fall '07
 YaoyunShi

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