Which of the following is a proposition ?

Options

A. I am a lion
B. A half open door is half closed
C. A triangle is a circle and 10 is a prime number
D. Logic is an intesting subject

Answer

To determine which of the given statements is a proposition, we first need to understand what a proposition is. A proposition is a declarative sentence that can be classified as either true or false, but not both.

Let's analyze each statement one by one:

1. **"I am a lion."**
- This statement is a declarative sentence. However, it cannot be classified as true or false universally because it depends on the context (i.e., whether the speaker is indeed a lion). Thus, it is not a proposition.

2. **"A door is half open half closed."**
- This statement is also a declarative sentence. However, it is ambiguous as it does not clearly state a true or false condition. A door cannot be half open and half closed at the same time in a strict sense. Therefore, this is not a proposition.

3. **"A triangle is a circle."**
- This statement is a declarative sentence that can be evaluated as false. A triangle and a circle are distinct shapes, and one cannot be the other. Thus, this is a proposition.

4. **"10 is a prime number."**
- This statement is a declarative sentence that can also be evaluated as false. The number 10 has factors other than 1 and itself (2 and 5), so it is not a prime number. Therefore, this is also a proposition.

Now, we can conclude that the statements "A triangle is a circle" and "10 is a prime number" are both propositions, as they can be definitively classified as false.

**Final Answer:**
The statements "A triangle is a circle" and "10 is a prime number" are propositions.

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