HW#2 CE 2305
Exercise 1.3
7)
a) All the comedians are funny.
b) All people are comedians and funny.
c) There exists one person if he/she is comedian then he/she is funny.
d) There exists one person who is comedian and is funny.
9)
a)
∃
x(P(x)
Q(x))
⋀
b)
∃
x(P(x)
¬Q(x))
⋀
c)
∀
x(P(x)
Q(x))
⋁
d)
∀
x¬(P(x)
Q(x))
⋁
25) Let P(x) = x is perfect and Q(x) = x is your friend and the domain be all the
people.
a)
∀
x¬P(x)
b) ¬
∀
x P(x)
c)
∀
x (Q(x)→P(x))
d)
∃
x(Q(x)
P(x))
⋀
e)
∀
xQ(x)
⋀
∀
xP(x)
f) (¬
∀
x Q(x))
(
⋁
∃
x¬P(x))
37)
a) Let P(x) = x qualifies as an elite flyer, Q(x) = x flies more than 25000 miles and
R(x) = x takes more than 25 flights during that year.
∀
x [(Q(x)
R(x)) → P(x)]
⋁
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HW#2 CE 2305
b) Let A(x) = x is a man, B(x) = x is a woman, C(x) = x qualifies for the marathon,
P(x) = x best time is less than 3 hours and Q(x) = x best time is less than 3.5 hours.
∀
x[[(A(x)
P(x)) → C(x)]
[(B(x)
Q(x)) → C(x)]]
⋀
⋀
⋀
c) Let A(x) = x must take at least 60 course hours, B(x) = x must take at least 45
course hours and write a master’s thesis, C(x) = x must receive a grade no lower
than a B in all required courses, D(x) = x will receive a master degree.
∀
x[[[A(x)
⋁
B(x)]
⋀
C(x)] →D(x)]
d) Let A(x) = x has taken more than 21 credit hours in a semester, B(x) = x
received all A’s.
∃
x[A(x)
⋀
B(x)]
41)
a) Let P(x,y) = Disk x has more than y kilobytes of free space, Q(x) = Mail
message x can be saved.
∃
xP(x,10)→
∃
xQ(x)
b) LetA(x) = Alert x is active, B(x) = Message x is queued and C(x) = Message x is
transmitted.
[
∃
xA(x)]→
∀
x[B(x)→C(x)]
c) Let P(x) = Diagnostic monitor tracks the status of system x and Q(x) = Status of
the main console.
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 Fall '10
 MRaz
 Math, Computer Science, Multiplication, Alice, Lola

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