Math 2534
Supplement problems for sec 1.31.4
1)
Let P be the set of all people and C the set of all cats. State in a natural worded
sentence the meaning of each of the following:
a)
(
∃
x
ε
P such that x loves Cats)
b)
(
∀
x
ε
P , x loves Cats)
c)
(
∃
x
ε
P such that
∀
y
ε
C, y loves x )
d)
(
∀
x
ε
P,
∃
y
ε
C such that
x loves y )
2)
If M = {1,2,3}, determine the truth value of each of the following propositions and
justify your answer.
a)
(
∀
x
ε
M, (x + 1)
2
= x
2
+ 1)
b)
(
∃
x
ε
M such that
x
2
+ x = 6)
c)
∼(∀
x
ε
M, x
2
+ x = 6)
d)
∼(∃
x
ε
M such that
x
2
+ 3x = 1)
3)
State which quantifiers, what sets and what conditions are involved in each of the
following statements.
a)
All differentiable functions are continuous.
b)
All's well that ends well.
c)
There are more things in heaven and earth, Horatio, than are dreamt of in your
philosophy.
d)
All that glitters is not gold.
4)
Let N be the set of all positives integers. State which of the following propositions
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 Spring '07
 MPMcQuain
 Math, Rational number, following propositions

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