UNIVERSITY OF WATERLOO
School of Computer Science
CS245
Logic and Computation
Spring 2009
TUTORIAL 4
1. Express the following English sentences as predicate logic formulas (Exercise 6.4 of text).
(a) All secondyear students are hardworking.
(b) No one can be clever without being hardworking.
(c) Clever students work hard.
(d) Those who do not work hard are lazy.
(e) The lazy students are exactly those who do not work hard.
(f) Not being lazy is equivalent to being hardworking.
(a)
∀
x
•
(
second
year
(
x
)
∧
student
(
x
))
⇒
hardworking
(
x
)
(b)
¬
(
∃
x
•
clever
(
x
)
∧ ¬
hardworking
(
x
))
(c)
∀
x
•
(
clever
(
x
)
∧
student
(
x
))
⇒
hardworking
(
x
)
(d)
∀
x
• ¬
hardworking
(
x
)
⇒
lazy
(
x
)
(e)
∀
x
•
(
lazy
(
x
)
∧
student
(
x
))
⇔ ¬
hardworking
(
x
)
(f)
∀
x
• ¬
lazy
(
x
)
⇔
hardworking
(
x
)
where
second
year
(
x
)
is true iff
x
is in second year
student
(
x
)
is true iff
x
is a student
clever
(
x
)
is true iff
x
is clever
hardworking
(
x
)
is true iff
x
is hardworking
lazy
(
x
)
is true iff
x
is lazy
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2. Express the following English sentences as predicate logic formulas (Exercise 6.8 of text).
(a) London stores only supply stores outside of London.
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 Spring '08
 WORMER
 Computer Science, Semantics, Predicate logic, Model theory, Firstorder logic, Domain of discourse

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