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 $y$.
Express the following by a simple English sentence. Avoid symbols and predicates in English sentences.
$\neg T(Bob, y)$"
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!