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I have a question about well-formed/well-defined predicates. Our class was presented with the following exercise:

Let ${S}$ denote the set of all students in your class, ${C}$ denotes the set of all countries, and $T(x, y)$ denotes that $x$ travels to country $y$.

<p>Express the following by a simple English sentence. Avoid symbols and predicates in  English sentences.</p>

<p>$\neg T(Bob, y)$"</p>

It seems to me that it is not appropriate to define only one of the variables in the predicate; it says "Bob does not travel to country $y$," but $y$ was never quantified or put in a domain (it doesn't say $y \in {C}$ -- so can we still assume $y$ is a country?), but our professor told us it was a 'valid open statement' the way it was written, and we could assume $y$ was a country.

I just wanted to know if it is in fact proper to symbolize things this way. I have looked at the other posts but am still not certain. There are similar examples ($"L(x,y)"$ standing for "$x$ likes $y$") that make me wonder if it is okay to write things this way. Clarification is appreciated. Thank you!

kldv
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  • To be very careful, one could add something like this: For $(x,y)\in S\times C$, $T(x,y)$ denotes that... Apparently your professor is not requiring that much formality in this one (which really is pretty clear from context). I note that in the question, it doesn't explicitly say that Bob is a student. – paw88789 Jan 31 '15 at 16:54
  • Thank you- you are right that the prof is not being very formal. Our task was to evaluate the sentence as is, and I said I thought that technically there was insufficient information to do so, but apparently that was not the right answer. – kldv Feb 01 '15 at 01:50

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