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EXAM 2
Unless noted otherwise let
L
be the
PC
0
language (with equality) generated by
the following:
H
(unary relation symbol),
L
(binary relation symbol), and
a,b,c
(constant symbols).
1.
True or False (2pts each)
The following refer to the semantics for
L
.
(1)
¬
(
a
≈
b
)
∧ ¬
(
b
≈
c
)

=
¬
(
a
≈
c
)
(2)
{{{}}}
and
{{}}
have the same number of elements.
(3) If
φ
∈ L
and
a
≈
a

=
φ
, then
φ
is a logical truth.
(4) If
I
=
h
U,
¯
H,
¯
L,
¯
a,
¯
b,
¯
c
i
is an interpretation of
L
such that
I

=
¬
(
a
≈
b
),
then
U
has at least two elements.
(5) If
A
and
B
are sets, then
A
×
B
=
B
×
A
.
1
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EXAM 2
2.
Evaluate (2pts each)
Let
I
be the interpretation of
L
that is given as follows:
•
U
=
{
0
,
1
,
2
,
3
,
4
}
•
¯
H
=
{
0
,
1
,
3
}
•
¯
L
=
{
(1
,
1)
,
(2
,
2)
,
(3
,
3)
,
(0
,
4)
,
(4
,
1)
,
(4
,
3)
}
•
¯
a
= 3,
¯
b
= 4, ¯
c
= 1
Evaluate the following with respect to interpretation
I
:
(1)
¬
(
a
≈
b
)
→ ¬
(
L
(
a,b
)
∨
L
(
b,a
))
(2) (
H
(
a
)
→
L
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 Spring '11
 H

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