1. **State the problem:** Identify which sentences are propositions and determine the truth value of each proposition. 2. **Definition:** A proposition is a declarative sentence that is either true or false but not both. 3. **Analyze each sentence:** a) "Boston is the capital of Massachusetts." - This is a declarative sentence. - Boston is indeed the capital of Massachusetts. - So, this sentence is a proposition and it is true. b) "Miami is the capital of Florida." - This is a declarative sentence. - Miami is not the capital of Florida (Tallahassee is). - So, this sentence is a proposition and it is false. c) "2 + 3 = 5." - This is a mathematical statement. - 2 plus 3 equals 5, which is true. - So, this sentence is a proposition and it is true. d) "5 + 7 = 10." - Mathematical statement. - 5 plus 7 equals 12, not 10. - So, this is a proposition and it is false. e) "x + 2 = 11." - This sentence contains a variable x, making it an open sentence. - It is not true or false until x is specified. - So, it is not a proposition. f) "Answer this question" - This is a command, not a declarative sentence. - Therefore, it is not a proposition. **Final answers:** - Propositions: a (true), b (false), c (true), d (false) - Not propositions: e, f