EECS 203 Homework 2
Section 1.3
1. (E) 6bef and 10cde
6a) Every student in school has visited North Dakota
6b) Not every student in the school has visited North Dakota
6c) No student in the school has visited North Dakota
10c)
∀
x
(
C
(
x
)
∧
F
(
x
)
∧ ¬
D
(
x
))
10d)
∀
x
¬
(
C
(
x
)
∧
D
(
x
)
∧
F
(
x
))
10e)
(
∃
xC
(
x
))
∧
(
∃
xD
(
x
))
∧
(
∃
xF
(
x
))
2. (M) 42abc
42a) Let A(x) mean ”user x has access to an electronic mailbox”
∀
xA
(
x
)
42b) Let S(x, y) mean ”system x is in y state”
∀
xS
(
filesystem, locked
) =
⇒
A
(
x
)
42c) Using prepositional function from part 42b
S
(
firewall, diagnostic
) =
⇒
S
(
proxyserver, diagnostic
)
3. (C) 44
We want P and Q that are sometimes false and sometimes true.
Let P(x) mean ”x is even”
Let Q(x) mean ”x is multiple of 3”
for two values in domain of integers, x = 4 and x = 9.
(
∀
x
(
P
(
x
))
⇐⇒
(
∀
x
(
Q
(
x
)))
reduces to
False
⇐⇒
False
and hence true. But
∀
x
(
P
(
x
)
⇐⇒
Q
(
x
))
is false. Hence two are not logically equivalent.
Section 1.4
4. (E) 6def
6d) Some student is enrolled in both Math222 and CS252.
6d) There are two distinct students such that second one is enrolled in all the courses that ﬁrst one is en
rolled in.
6d) There are two distinct students that are enrolled in the same courses.
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 Spring '07
 YaoyunShi
 Logic, Predicate logic, North Dakota, universal instantiation, Premise Premise Existential

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