Which of the following is an open curve?

Options

A.
B.
C.
D.

Answer

To determine which of the given options is an open curve, we need to understand the definitions of open and closed curves.

### Step-by-Step Solution:

1. **Definition of Open Curve**: An open curve is a curve where the endpoints are not connected. This means that if you were to draw the curve, you would have two distinct endpoints that do not meet.

2. **Definition of Closed Curve**: A closed curve is one where the endpoints are connected, forming a complete loop or shape. In a closed curve, if you start drawing from one point, you can return to that same point without lifting your pencil.

3. **Analyzing the Options**:
- **Option 1**: Check if the endpoints are connected. If they are, it is a closed curve.
- **Option 2**: Again, check for connection of endpoints. If they are connected, it is a closed curve.
- **Option 3**: Similar to the previous options, check if the endpoints are connected.
- **Option 4**: Look for a gap between the endpoints. If there is a gap, it indicates that the endpoints are not connected, making it an open curve.

4. **Identifying the Correct Option**: After examining all options:
- If any option shows a gap between the endpoints, that option is the open curve.
- If all endpoints are connected in the other options, they are closed curves.

5. **Conclusion**: Based on the analysis, the option with the gap between the endpoints is the open curve.

### Final Answer:
The correct answer is **Option 4**, as it is the only option where the endpoints are not connected, indicating it is an open curve.

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