[Math] How to determine a sentence is proposition or not

Question

I want to know how to determine that a sentence is proposition or not. What is the condition.
And also want to know that.
From Below sentences which are proposition or not
1.Today is Friday
2.He is a good boy
3.john is a good boy.

Answer 1

A proposition is a claim; something that is true or false.

All these three are sentences that can be used to express propositions, although the context will have to make clear exactly what is being claimed. For example, the first claim's truth-value depends on what day you make that claim, the second depends on what 'he' is referring to, and even when you use 'John' in the third sentences, the context will have to make clear which of the many 'John's you are talking about. Moreover, what exactly constitutes a 'good boy'?

Some texts will say that because of these ambiguities or unresolved indexicals, none of these are propositions. Other texts may say that 'He is a good boy' is not, but 'John is a good boy' is. Also, some texts carefully differentiate between 'sentences' as actual utterances of natural language, while 'propositions' are the abstract idea expressed by those sentences (thus, a single proposition can be expressed by many different sentences). Other texts, however, do not make any such distinction.

So, there is a lot of confusion and disagreement on exactly when a sentence is, or expresses, a proposition ... which is really too bad, since the basic concept of a proposition as a claim rather than, say, a question or just a single word, should be completely intuitive, and all you really need to dive into propositional logic.

Indeed, these kinds of exercises typically become more of a pedantic exercise in figuring out what the author/instructor wants you to say, rather than teaching you some important concept you didn't already know.

My advice: take a good look at the examples the author or instructor gave to you, and that should tell you what answer they are looking for.