ECS 20: Homework 2 Solutions
Instructor: Prof.Max TA: Yuxi Hu
Page 4650
8a. If an animal is a rabbit, then that animal hops.
8b. Every animal is a rabbit and hops.
10a.
∃
x
(
C
(
x
)
∧
D
(
x
)
∧
F
(
x
))
10c.
∃
x
(
C
(
x
)
∧¬
D
(
x
)
∧
F
(
x
))
14a. Since (

1)
3
=

1, this is true
14d. Twice a positive number is larger than the number, but this inequality is not true
for negative numbers or 0. Therefore
∀
x
(2
x > x
) is false.
Page 7274
4a. Simpliﬁcation.
4b. Disjunctive syllogism.
10a. If we use modus tollens starting from the back, then we conclude that I am not
sore. Another application of modus tollens then tells us that I did not play hockey.
14d.Let
c
(
x
) be
x
is in this class, let
f
(
x
) be
x
has been to France, and let
l
(
x
) be
x
has visited the Louvre. We are given premises
∃
x
(
c
(
x
)
∧
f
(
x
)),
∀
x
(
f
(
x
)
→
l
(
x
)). We want
to conclude
∃
x
(
c
(
x
)
∧
l
(
x
)). In the proof,
a
represents an unspeciﬁed particular person.
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 Spring '09
 Khoel
 Negative and nonnegative numbers, conditional statement, Modus tollens

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