Rob Bayer
Math 55 Worksheet
June 23, 2009
Instructions
•
Introduce yourselves! Despite popular belief, math is in fact a team sport!
•
Find some blackboard space, a piece of chalk, and decide who will be your ﬁrst scribe.
•
Do the problems below, having a diﬀerent person be the scribe for each one.
•
Try to work out the problems as a group, but feel free to ﬂag me down if you run into a wall.
Predicates and Quantiﬁers
1. If
P
(
x
) is the statement “x
>
0” and
G
(
x,y
) is the statement
x
2
≥
y
, determine the truth value of each of the
following
(a)
P
(1)
(b)
G
(2
,

3)
(c)
P
(

1)
→
G
(

2
,
1)
2. Using the same predicates as above, determine the truth values of each of the following statements if the
domain is the set of all real numbers.
(a)
∀
xP
(
x
)
(b)
∃
xP
(
x
)
∧ ∀
xG
(
x,
0)
(c)
∃
yG
(2
,y
)
3. Suppose the domain of
P
(
x
) consists of the integers 0,1,2,3. Rewrite each of the following statements without
using quantiﬁers:
(a)
∀
xP
(
x
)
(b)
∃
x
(
x
6
= 1
∧
P
(
x
))
(c)
∀
x
(
x
6
= 1
→ ¬
P
(
x
))
4. Let
S
(
x
) be the statement “
x
is a student,”
L
(
x
) be “
x
lives in Germany”
G
(
x
) be “
x
speaks German.”
Translate each of the following into English or into logic symbols as appropriate. The domain is the set of all
people.
(a)
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 Summer '08
 STRAIN
 Math, Logic, following statements, Quantification

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