ECEN 601: Assignment 2
Problems:
1. Suppose that the possible values of
x
and
y
are all cars. Let
L
(
x,y
) = “
x
is as fast as
y
,” let
M
(
x,y
) = “
x
is as expensive as
y
” and
N
(
x,y
) = “
x
is as old as
y
.” Translate the following
statements into words.
(a) (
∃
x
)(
∀
y
)
L
(
x,y
).
(b) (
∀
x
)(
∃
y
)
M
(
x,y
).
(c) (
∃
y
)(
∀
x
)[
L
(
x,y
)
∨
N
(
x,y
)].
(d) (
∀
y
)(
∃
x
)[
¬
M
(
x,y
)
→
L
(
x,y
)].
2. Suppose that the possible values of
p
and
q
are all fruit. Let
A
(
p,q
) = “
p
tastes better than
q
,” let
B
(
p,q
) = “
p
is riper than
q
” and
C
(
p,q
) = “
p
is the same species as
q
.” Translate the
following into symbols.
(a) There is a fruit such that all fruit taste better than it.
(b) For every fruit, there is a fruit that is riper than it.
(c) There is a fruit such that all fruit taste better than it and are not riper than it.
(d) For every fruit, there is a fruit of the same species that does not taste better than it.
3. Write a negation of each statement. Do not write the word “not” applied to any of the objects
being quantified (for example, do not write “Not all boys are good” for the first part).
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 Fall '08
 Staff
 Trigraph, Rational number, possible values

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