Unless a statement is provable, it cannot be judged as true or false. A provable statement is one that can be proven with additional facts or reasoning. A statement that is simply an assertion or belief, however, carries no determinate truth value.
For example, the utterance "I am the walrus" does not have any specific truth value, even though it is a grammatical statement and can be evaluated in terms of its logical validity. An assertion can also be a hypothesis, which is an assumption that has not yet been tested. For instance, if you were to say to someone, "I think it will rain tomorrow," that statement could be either true or false, depending on how much evidence the person has in support of their claim.
In mathematics, a theorem is a set of statements that imply each other and have a logically consistent truth value. In other words, it is a set of if-then statements. If one of the if-then statements is a tautology, which is a statement that can only be true or false, then the entire theorem must be true.
It is important to recognize if-then statements because they are a key part of solving mathematical problems. When determining whether or not a statement is true, it is often helpful to read it without any qualifiers such as "always," "never," and "cannot." This can help eliminate confusion and make it easier to determine the truth value of a statement.