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CS
372
Homework 3
Due date:
In class Thusrday Feb. 28, 2008
By email Sunday 12:59 p.m. to Robert Xiao (
rkx2@cornell.edu
)
use subject line (HWK#3 – CS372)
SHOW YOUR WORK FOR ALL QUESTIONS
1
–
Determine the truth value of each of these statements if the domain of each variable
consists of all real numbers
a)
!
x
"
y (x
2
=y)
True (y = x
2
)
b)
!
x
"
y (x = y
2
)
False (if x is negative no such y exists)
c)
"
x
!
y (xy = 0)
True (x=0)
d)
"
x
"
y (x + y
#
y + x)
False (communtative law for addition alwyas holds)
e)
!
x ( x
#
0
$
"
y (xy = 1))
True (let y = 1/x)
f)
"
x
!
y (y
#
0
$
xy = 1)
False (the reciprocal of y depends on y; there is not one x that works for all y)
g)
!
x
"
y ( x + y = 1)
True
(y = 1x)
h)
"
x
"
y (x + 2y = 2
%
2x + 4y = 5)
False (inconsistent system of equations)
i)
!
x
"
y (x+ y = 2
%
2x – y = 1)
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View Full DocumentFalse (this system of equations has only one solution; e.g.,
if x=0n no y satisfies y =2 and
–y = 1)
j)
!
x
!
y
"
z (z = (x+y)/2)
True
(z = (x+y) /2)
2
Let F(x,y) be the statement “x can fool y”, where the domains consists of all people in
the world. Use quantifiers to express each of these statements:
a)
Everybody can fool Fred
!
(x) F(x Fred)
b)
Evelyn
can fool everybody
!
(y) F(Evelyn, y)
c)
Everybody can fool somebody
!
x
"
y F(x y)
d)
There is no one who can fool everybody
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 Spring '07
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