A proposition is a mathematical statement such as "3 is greater than 4," "an infinite set exists," or "11 is prime."
With sufficient information, mathematical logic can often categorize a proposition as true or false, although there are various exceptions
I was thinking about saying, "Perhaps doing injustice to the philosophy of mathematics..." OK, I can very well accept defining a proposition purely syntactically as a well-formed sentence with no free (unbound) variables.
Why don't you like the question? I think it is important for students to distinguish between terms and sentences and to identify free variables. I often see people writing things like "Induction step: prove k + 1" and using variables that are not properly introduced.