Logic is usually studied through language. In formal logic, we attached a symbol (e.g. \(S\)) to a statement (e.g. “Socrates is a man”). This statement has a truth value: either Socrates is a man, and \(S\) is true, or Socrates isn’t a man, and \(S\) is false. We call this kind of statement a proposition. In classical logic, there is no middle ground: either a proposition is true, or false. This is the law of excluded middle.
By definition, a proposition could be attached to any statement, as long as it has a truth value. For example, “Socrates is a man” or “The Moon is made of cheese”. We usually don’t care if the statement is true or false, only that it can be true or false.
Logic is the study of correct arguments.