At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
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.
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.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
