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Section 2.3
37
7. [BB]
The argument assumes that for
a
E
n
there exists a
b
such that
(a,
b)
En. This need not be the
case: See Exercise 5(g).
8. (a)
[BB]
Reflexive: Every word has at least one letter in common with itself.
Symmetric:
If
a
and
b
have at least one letter in common, then so do
b
and
a.
Not antisymmetric: (cat, dot) and (dot, cat)
are
both in the relation but dot
=F
cat!!
Not transitive: (cat, dot) and (dot, mouse)
are
both in the relation but (cat, mouse) is not.
(b) Reflexive: Let
a
be a person.
If
a
is not enrolled at Miskatonic University, then
(a, a)
E
n.
On
the other hand, if
a
is enrolled at MU, then
a
is taking at least one course with himself, so again
(a, a)
En.
Symmetric:
If
(a,
b)
E
n,
then either it is the case that neither
a
nor
b
is enrolled at MU (so
neither is
b
or
a,
hence,
(b, a)
E
n)
or it is the case that
a
and
b
are both enrolled and
are
taking
at least one course together
(in
which caseb and
a
are enrolled and taking a common course, so
(b, a)
En). In any case, if
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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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