Exam # _______
Name_______________________________
Score _________/ 64
CS 1502 Spring 2007 Exam 1
Solutions
.
There are
9
problems on
8
pages with a total score of
64
.
Page 8 contains some proof rules that
you can refer to.
Do all problems.
1.
(8 points) Translate the following sentences into logic.
(a) Object
a
is in front of
b
if
b
is small.
If
b
is small, then
a
is in front of
b
.
Small(b)
→
FrontOf(a,b)
(b) Object
c
is large only if
d
is between object
b
and object
a
.
If
c
is large, then
d
is between
b
and
a
.
Large(c)
→
Between(d,b,a)
(c) If
a
is a tetrahedron, then it is neither in the same row as
b
nor the column as
c
.
Tet(a)
→
¬
(SameRow(a,b) \/ SameCol(a,c))
(d) Neither
a
nor
b
is cube, but they have the same shape as
c
.
¬
(Cube(a) \/ Cube(b)) /\ SameShape(a,c) /\ SameShape(b,c)
2.
(6 points) Consider the argument below.
Determine whether the conclusion is a
tautological consequence
of the premises.
Support your answer using a
truth table
and an
interpretation of the result from the truth table.
Your answer must show that you understand
what a tautological consequence is.
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 Spring '11
 NeilTennant
 Logic, #, Dodec, following valid argument, formal fitch proof

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