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2
Solutions to Exercises
(c) [BB] True (the hypothesis
is false).
(d) False (hypothesis is true, conclusion is false).
(e) [BB] False (hypothesis is true, conclusion is false: v'4
=
2).
(0
True
(g) [BB] True
(h) True
(i) EBB] True (the hypothesis is false:
.fX2
= Ixl)
G) True
(k)
[BB] False
(I)
True
5. (a) [BB]
a
2
~
0 and
a
is a real number (more simply,
a
=
0).
(b)
x
is not real or
x
2
+
1
f:.
0 (more simply,
x
is any number, complex or real).
(c) [BB]
x f:.
1 and
x f:.
1.
(d) There exists an integer which is not divisible by a prime.
(e) [BB] There exists a real number
x
such that
n
::;
x
for every integer
n.
(0
(ab)c
=
a(bc)
for all
a, b,
c.
(g) [BB] Every planar graph can be colored with at most four colors.
(h) Some Canadian is a fan of neither the Toronto Maple Leafs nor the Montreal Canadiens.
(i) There exists
x
>
0
and some
y
such that
x
2
+
y2
~
o.
G)
x
:2:
2 or
x
~
2.
(k) [BB] There exist integers
a
and
b
such that for all integers
q
and
r, b f:. qa
+
r.
(1) [BB] For any infinite set, some proper'subset
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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