Which of the following is a **well-defined set** (in the mathematical sense)?
AThe collection of ten most talented writers of India.
BA team of eleven best cricket batsmen of the world.
CThe collection of all natural numbers less than 100.
DA collection of most dangerous animals of the world.
Answer & Solution
Correct answer: C. The collection of all natural numbers less than 100.
A set requires a **well-defined** rule for membership: given any object, we must be able to decide *unambiguously* whether it belongs to the set.
- **A, B, D**: words like *most talented*, *best*, and *most dangerous* are subjective — different people would judge differently. So these are *not* well-defined.
- **C**: *natural numbers less than 100* is precise. For any object, we can check (1) whether it is a natural number and (2) whether it is less than 100. Unambiguous → well-defined set.
This is NCERT Class 11, Exercise 1.1 Q1.
Related questions
Penalty for wrong answers : THERE WILL BE PENALTY FOR WRONG ANSWERS MARKED BY A CANDIDATE Penalty for wrong answers : THERE WILL BE PENALTY FOR WRONG ANSWERS MARKED BY A CANDIDATE For [[1,2],[2,4]], the determinant equals:If A is invertible, |A^{−1}| equals:For a 3 × 3 non-singular A with |A| = 5, the value of |adj A| is:For a non-singular square matrix A of order n, |adj A| equals:For non-singular A, B of the same order, (AB)^{−1} equals:For a non-singular A, (A^{−1})^{−1} equals: