ASSIGNMENT 6
MATH 303, FALL 2011
Instructions:
Do at least
3 points from each section
and at least
10 points total
.
Up to 12 points will be graded, but your maximum score is 10. If you hand in more than 12
points please indicate which ones you want graded, otherwise the first 12 will be graded.
Manipulation
(M1)
(1 point)
Let
c
and
c
0
be constant symbols. Show that
∃
x
(
((
c
=
x
)
∧
(
x
=
c
0
))
→
c
=
c
0
)
is valid using Cohen’s rules (state explicitly which rules you use).
(M2)
(2 points)
Let
A
(
x
) be a well formed formula with free variable
x
and let
B
be a
well formed formula with no occurence of
x
. Let
c
be a constant symbol and let
S
=
{∀
xA
(
x
)
, A
(
x
)
→
B
}
Show that you can derive
B
from
S
.
Use
only
Cohen’s rules, and state explicitly
which rules you use in your derivation.
(M3)
(1 point)
Let
E
=
{
a, b, c, d
}
. Let
X
=
P
(
E
)
 {{
a, b
}
,
∅}
. What are the maximal
elements of
X
?
What are the minimal elements of
X
?
Does
X
have a smallest
element? Does
X
have a largest element?
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 Spring '11
 RWK
 Math, Order theory, Natural number, Partially ordered set, Cardinal number, Maximal element

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