Which of the following are sets? Justify your answer.
The collection of all the months of a year beginning with the letter J.
Yes, this is a set. The collection is well-defined as we can clearly identify the months: January, June, and July. There is no ambiguity in determining which months belong to this collection.
The collection of ten most talented writers of India.
No, this is not a set. The term 'most talented' is subjective and varies from person to person. Different individuals may have different opinions about who the most talented writers are, making this collection not well-defined.
A team of eleven best-cricket batsmen of the world.
No, this is not a set. The term 'best' is subjective. Different people may have different criteria for selecting the best batsmen, leading to ambiguity in determining who belongs to this collection.
The collection of all boys in your class.
Yes, this is a set. The collection is well-defined as we can clearly identify all boys in a specific class. There is no ambiguity in determining membership.
The collection of all natural numbers less than 100.
Yes, this is a set. The collection is well-defined as natural numbers less than 100 can be precisely identified: {1, 2, 3, ..., 99}. Every number can be clearly determined to belong or not belong to this collection.
A collection of novels written by the writer Munshi Prem Chand.
Yes, this is a set. The collection is well-defined as the novels written by Munshi Prem Chand can be clearly identified. There is no ambiguity in determining which novels belong to this collection.
The collection of all even integers.
Yes, this is a set. The collection is well-defined as even integers can be precisely identified: {..., -4, -2, 0, 2, 4, ...}. Every integer can be clearly determined to be even or not.
The collection of questions in this Chapter.
Yes, this is a set. The collection is well-defined as all questions in this Chapter can be clearly identified and listed. There is no ambiguity.
A collection of most dangerous animals of the world.
No, this is not a set. The term 'most dangerous' is subjective and varies based on different criteria. Different people may classify different animals as dangerous, making this collection not well-defined.
Explanation
A set is defined as a well-defined collection of distinct objects. The key criterion is that the collection must be 'well-defined' - meaning we should be able to clearly and objectively determine whether an object belongs to the collection or not. Collections with subjective terms like 'most talented', 'best', or 'most dangerous' are not well-defined and hence not sets. Collections with clear, objective criteria like 'months beginning with J', 'natural numbers less than 100', or 'novels written by a specific author' are well-defined and hence are sets.