Which option is not an example of a well-defined set?
Answer and explanation
Correct answer: {x : x is a beautiful number}
A set is well-defined when there is an objective rule for deciding whether any particular object belongs to it. Even natural numbers below 20, integer solutions of x² = 4, and English vowels can all be identified unambiguously. However, “beautiful number” has no universally accepted mathematical definition and depends on personal opinion. Therefore, option B is not a well-defined set.
Frequently asked questions
What is the correct answer to this question?
{x : x is a beautiful number}
Why is this the correct answer?
A set is well-defined when there is an objective rule for deciding whether any particular object belongs to it. Even natural numbers below 20, integer solutions of x² = 4, and English vowels can all be identified unambiguously. However, “beautiful number” has no universally accepted mathematical definition and depends on personal opinion. Therefore, option B is not a well-defined set.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
