Which of the follwing collection of objects is not a set? (i) The collection of all even integers. (ii) The collection of all months of a year beginning with letter J. (iii) The collection of most talented writers of India. (iv) The collection of all prime numbers less than 20.

Options

A. The collection of all even integers.
B. The collection of all months of a year beginning with letter J.
C. The collectionn of most talented writers of India.
D. The collection of all prome numbers less than 20.

Answer

To determine which of the following collections of objects is not a set, we will analyze each option based on the definition of a set. A set is a well-defined collection of distinct objects, where it is clear whether an object belongs to the collection or not.

1. **Option (i): The collection of all even integers.**
- This is a set because it is well-defined. We can clearly identify all even integers (e.g., ..., -4, -2, 0, 2, 4, ...).

2. **Option (ii): The collection of all months of a year beginning with the letter J.**
- This is also a set. The months that start with J are January and June. This collection is well-defined and finite.

3. **Option (iii): The collection of most talented writers of India.**
- This is not a set. The term "most talented" is subjective and does not provide a clear criterion for inclusion. Different people may have different opinions on who qualifies as a "most talented" writer, making it ambiguous.

4. **Option (iv): The collection of all prime numbers less than 20.**
- This is a set because it is well-defined. The prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19.

Based on this analysis, the collection that is not a set is:

**Answer: (iii) The collection of most talented writers of India.**