Which of the following is a singleton set ?

Options

A. The set of all the months in a year having exactly 30 days.
B. The set of all the days in a week.
C. The set of all the natural satellites of the earth in the solar system.
D. The set of all the intersecting points of two parallel lines in a plane.

Explanation

To determine which of the given options is a singleton set, we need to understand what a singleton set is. A singleton set is a set that contains exactly one element. Let's analyze each option step by step.

### Step-by-Step Solution:

1. **Identify the Definition of a Singleton Set:**
- A singleton set is defined as a set that contains only one element.

2. **Examine the Options:**
- We have four options to evaluate.

3. **Option A: The set of all months in a year having exactly 30 days.**
- The months with 30 days are April, June, September, and November.
- Count of elements: 4 (April, June, September, November).
- Since there are 4 elements, this is **not a singleton set**.

4. **Option B: The set of all the days in a week.**
- The days of the week are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday.
- Count of elements: 7 (Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday).
- Since there are 7 elements, this is **not a singleton set**.

5. **Option C: The set of all the natural satellites of Earth in the solar system.**
- The only natural satellite of Earth is the Moon.
- Count of elements: 1 (Moon).
- Since there is 1 element, this **is a singleton set**.

6. **Option D: The set of all the intersecting points of two parallel lines.**
- Parallel lines do not intersect.
- Count of elements: 0 (no intersecting points).
- Since there are 0 elements, this is an **empty set**, not a singleton set.

7. **Conclusion:**
- The only option that qualifies as a singleton set is **Option C**: The set of all the natural satellites of Earth in the solar system.

### Final Answer:
**Option C: The set of all the natural satellites of Earth in the solar system is a singleton set.**

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