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Subject: "A strange question"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #251
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Ralph Boles
Jul-21-03, 07:26 AM (EST)
"A strange question"
   Consider the following relation on the set of all people.

a R b <--> a and b have visited the same cities.

is R transitive i.e. (aRb and bRc -->aRc) ?

1) No.

a has visited Rome, paris, london
b has visited rome, paris, New York
c has visited paris, New York, Honolulu

then aRb since they have visited the same cities (Rome, Paris)
bRc (paris, New York)

but a is not related to c since they have only one city in common not "cities" as required.

2) Yes.

"have visited the same cities" means that the set of cities visited by a and b is the same. obviously trnasitive.

Basically the question reduces to wether there is an invisible "all" sitting in the phrase "have visitied (all) the same cities."

I think in math the convention is that there is never an implicit all, and in English in this case, there is an implicit "all."

what do you (all) think?

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Michael Klipper
Jul-21-03, 09:33 AM (EST)
1. "RE: A strange question"
In response to message #0
   I personally disagree. If you were to hand me this question, I would interpret the implicit "all", even in the mathematical sense.

If you wanted to phrase this so that I did not think you meant "all", you would want to say "a R b if a and b have visited cities in common" or "visited some cities together".

You do raise a good point, however, in making sure that one is able to correctly distinguish universal from existential quantifiers, particularly in plain language.

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