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CS 245 Winter 2009
Solution Set for Lecture 7
Kelly Ch. 2
Note:
The solutions in Kelly don’t number lines and list the rules used in each step. You
should do this in your semantic tableaux proofs.
Exercise 2.1 (p. 36)
1. In Kelly.
2. The set of formulas is consistent. One satisfying assignment is:
v
(
A
) = T
,v
(
B
) = T
3.
1.
A
⇒
B
2.
A
∨
B
3.
¬
B
4.
¬
A
IMPLIES 1
5.
A
CLOSED 4,5
OR 2
6.
B
CLOSED 3,6
7.
B
CLOSED 3,7
Because the tableau is closed, the set of formulas is inconsistent.
4. The set of formulas is consistent. One satisfying assignment is:
v
(
A
) = F
,v
(
B
) = F
5. The set of formulas is consistent. One satisfying assignment:
v
(
A
) = F
,v
(
B
) = T
,v
(
C
) = T
,v
(
D
) = T
1
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View Full Document 6.
1.
A
⇒
B
2.
B
⇒
C
3.
C
⇒
D
4.
A
∧¬
D
5.
A
6.
¬
D
AND 4
7.
¬
A
CLOSED 5,7
IMPLIES 1
8.
B
9.
¬
B
CLOSED 8,9
IMPLIES 2
10.
C
11.
¬
C
CLOSED 10,11
IMPLIES 3
12.
D
CLOSED 6,12
Because the tableau is closed, the set of formulas is inconsistent.
7. In Kelly.
8. The set of formulas is consistent. One satisfying assignment is:
v
(
A
) = T
,v
(
B
) = F
,v
(
C
) = F
9. The set of formulas is consistent. A satisfying assignment is given by
v
(
A
) = F
,v
(
B
) = T
,v
(
C
) = T
10. Error in text. The set of formulas is consistent. A satisfying assignment is given by
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This note was uploaded on 10/23/2009 for the course CS 245 taught by Professor A during the Spring '08 term at Waterloo.
 Spring '08
 A

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