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Chapter 12: Hints and Selected Solutions
Section 12.3 (page 327)
12.1
The argument is valid and the proof is a good one. In the following,
we repeat the proof, but being explicit about the proof methods being
used.
∀
x
[(
Brillig
(
x
)
∨
Tove
(
x
))
→
(
Mimsy
(
x
)
∧
Gyre
(
x
))]
∀
y
[(
Slithy
(
y
)
∨
Mimsy
(
y
))
→
Tove
(
y
)]
∃
xSlithy
(
x
)
∃
x
[
Slithy
(
x
)
∧
Mimsy
(
x
)]
Proof:
By the third premise, we know that something in the
domain of discourse is slithy. In order to use
∃
Elim
, let
b
be
one of these slithy things. By the second premise, everything
that is either slithy or mimsy is tove. Hence, by
∀
Elim
,
∨
Intro
and
→
Elim
, we know that
b
is a tove. By the ﬁrst
premise, using the same methods, we see that
b
is mimsy and
gyre. Hence
b
is mimsy, using
∧
Elim
. Thus,
b
is both slithy
and mimsy, using
∧
Intro
. Hence, something is both slithy
and mimsy, by
∃
Intro
.
12.4
The argument is valid. We give an informal proof.
∀
y
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 Spring '09
 dhoe
 Logic

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