CS 245 Winter 2009
Lecture 15 – Suggested Exercises
SOLUTION SET
1. Formalize the following sentences in predicate logic with equality. Show the English
phrases that your predicates and functions represent.
(a) There are three cars in the parking lot.
(b) The only one who made it to school in the snow storm was George.
(c) The only person who could be the CEO is George’s daughter.
(d) The person who won the award is the tallest person on some university basketball
team.
Soln:
(a)
∃
x,y,z
•
car
(
x
)
∧
inlot
(
x
)
∧
car
(
y
)
∧
inlot
(
y
)
∧
car
(
z
)
∧
inlot
(
z
)
∧¬
(
x
=
y
)
∧¬
(
x
=
z
)
∧ ¬
(
y
=
z
)
where
•
car
(
x
) – means
x
is a car
•
inlot
(
x
) – means
x
is in the parking lot
(b)
SSS
(
George
)
∧ ∀
x
•
SSS
(
x
)
⇒
(
x
=
George
)
where
•
SSS
(
x
) – means that
x
made it to school in the snow storm.
(c)
∀
x
•
CEO
(
x
)
⇒
x
=
daughter
(
George
)
where
•
CEO
(
x
) – means that
x
could be the CEO.
•
daughter
(
x
) – is the daughter of
x
.
(d)
∃
x
•
award
winner
(
x
)
∧∃
t
•
onteam
(
x,t
)
∧∀
p
•
onteam
(
p,t
)
∧¬
(
x
=
p
)
⇒
taller
(
x,p
)
where
•
award
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 Spring '08
 A
 Logic, Natural deduction, logical consequence

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