Let's analyze each given sentence to determine which ones are propositions and their respective truth values.
A proposition is a declarative sentence that is either true or false but not both.
1. "123 is a prime number."
- This is a proposition because it is making a declarative statement that can be either true or false.
- Truth value: False. 123 is not a prime number.
2. "2 is an even number."
- This is a proposition because it asserts a factual statement that can be either true or false.
- Truth value: True. 2 is an even number.
3. "Multiply \(5x + 2\) by 3."
- This is not a proposition. It is an instruction rather than a declarative sentence that can be judged true or false.
4. "Therefore 0 is an even number."
- This is a proposition because it is making a declarative statement that can be either true or false.
- Truth value: True. 0 is an even number.
5. "What an impossible question!"
- This is not a proposition. It is an exclamatory sentence, expressing emotion rather than stating a fact that can be judged as true or false.
6. "What an impossible question! ?"
- This is also not a proposition. It is an exclamatory sentence with a question mark, expressing emotion or surprise rather than stating a factual proposition.
7. "A triangle has four sides."
- This is a proposition because it is asserting a statement that can be judged true or false.
- Truth value: False. A triangle has three sides.
8. "Give me that book."
- This is not a proposition. It is a command rather than a declarative statement that can be judged true or false.
9. "x^2 - 4 = 0."
- This can be seen as a statement, but without specifying the value of \( x \), the truth value cannot be determined. It is more an equation awaiting a solution rather than a proposition that is definitively true or false within the provided context.
10. "What is your name?"
- This is not a proposition. It is a question, which cannot be adjudged as true or false.
Summary:
- "123 is a prime number." - Proposition, False.
- "2 is an even number." - Proposition, True.
- "Multiply \(5x + 2\) by 3." - Not a proposition.
- "Therefore 0 is an even number." - Proposition, True.
- "What an impossible question!" - Not a proposition.
- "What an impossible question! ?" - Not a proposition.
- "A triangle has four sides." - Proposition, False.
- "Give me that book." - Not a proposition.
- "x^2 - 4 = 0." - Not a simple proposition due to lack of context.
- "What is your name?" - Not a proposition.
