Are all sentences that are true or false a statement?

It's a bit more nuanced than that. While all statements are either true or false, not all sentences that are true or false are necessarily statements. Here's why:

Statements are declarative sentences that can be objectively evaluated as true or false. They express a proposition, a claim about the world.

Examples of statements:

* The Earth is round. (True)

* The sky is green. (False)

* The capital of France is Paris. (True)

Sentences that are true or false, but not statements:

* Questions: "Is the sky blue?" (This asks for information, not a claim.)

* Commands: "Close the door." (This gives an instruction, not a proposition.)

* Exclamations: "Wow, that's amazing!" (This expresses an emotion, not a claim.)

* Incomplete sentences: "The cat..." (This lacks a complete thought.)

Key takeaway: A sentence must express a proposition that can be judged as true or false to qualify as a statement.