40
Solutions to Exercises
13. Now the second binary relation would have an extra term, {Mike, 120}, and the third would have the
extra term, {Pippy Park, 120}. But, in addition, the entry {Pippy Park, 74} would be deleted. So Mike
is now clearly identified as the one who shot 120, and Pippy Park is where that occurred. Hence,
Mike's round of 74 was at Clovelly. Since Edgar has only one entry in binary relation two, he must
have shot 72 at both courses. Finally, Bruce's 74 must have been at Clovelly and hence his 72 was at
Pippy Park. All information has been retrieved in this case.
Exercises
2.4
1. Reflexive: For any citizen
a
of New York City, either
a
does not own a cell phone (in which case
a
rv
a)
or
a
has a cell phone and
a's
exchange is the same as
a's
exchange (in which case again
a
rv
a).
Symmetric:
If
a
rv
b
and
a
does not have a cell phone, then neither does
b,
so
b
rv
a;
on the other
hand, if
a
does have a cell phone, then so does
b
and their exchanges are the same, so again,
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 Summer '10
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 Graph Theory, Addition, Equivalence relation, Transitive relation, cell phone, Pippy Park

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