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I like this exercise. What is the definition of a proposition?

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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

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A proposition is a statements that is either true or false. An important point for this problem is that a proposition does not require values of some variables to become true or false; it already is.

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Originally Posted by emakarov
A proposition is a statements that is either true or false. An important point for this problem is that a proposition does not require values of some variables to become true or false; it already is.
FIY: Benson Mates and also here, spent most of one chapter of a textbook saying that there are no propositions just sentences.

BTW, I really don't like the question in the OP.

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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.

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Originally Posted by emakarov
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.
It is poorly written. I realize it is from UAE. But you reply #2 is right on. Without know what the author means by proposition, some int that list make no sense.