Spring2011
CMSC 250: HW 4
Due: Wed Feb 23 at Beginning of Rec
1. (0 points) What is your name? Write it clearly. Staple your HW.
2. (10 points) Write the following English sentences in predicate logic.
You can fool some of the people all of the time, and you can fool all of the people some of
the time, but you can’t fool all of the people all of the time.
Use
F
(
p, t
) for person
p
fooled at time
t
.
SOLUTION TO PROBLEM 2
(
∃
p
)(
∀
t
)[
F
(
p, t
)]
∧
(
∀
p
)(
∃
t
)[
F
(
p, t
)]
∧ ¬
(
∀
p
)(
∀
t
)[
F
(
p, t
)]
.
3. Consider the statement
All that glitters is not gold.
Throughout this problem use
GL
(
x
) for
x
glitters and
GO
(
x
) for
x
is gold.
(a) Write this statement using predicate logic if it is to be interpreted literally.
SOLUTION TO PART 3a
(
∀
x
)[
GL
(
x
)
→ ¬
GO
(
x
)]
.
(b) Write the statement using prediate logic with the intended meaning.
SOLUTION TO PART 3b
(
∃
x
)[
GL
(
x
)
∧ ¬
GO
(
x
)]
.
4. (30 points)
For this problem the domain is the natural numbers (includes 0). You may use +
,
×
.
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 Spring '08
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 Addition, A. Note, one bit, four bits, 9 bits, fourbit

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