Which of the following collections are sets ?

(i) All books in your school library.

(ii) All red flowers in a park.

(iii) All good players in your school.

(iv) All fiction movies.

(v) All easy problems in your book on mathematics.

(vi) All poor people in Mumbai.

(vii) All boys in your class weighing less than 50 kg.

(viii) All persons of repute in your colony.

(ix) All even numbers greater than 100.

(x) All integers less than -5.

(i) All books in your school library.

The collection is well-defined because one can objectively check if a book belongs to the library's catalog.

∴ It is a set.

(ii) All red flowers in a park.

Colour is a physical property that can be objectively identified.

∴ It is a set.

(iii) All good players in your school.

The term "good" is subjective; a player considered good by one person might not be considered good by another.

∴ It is not a set.

(iv) All fiction movies.

The genre of a movie is a defined category.

∴ It is a set.

(v) All easy problems in your book on mathematics.

The term "easy" is relative; a problem that is easy for one student may be difficult for another.

∴ It is not a set.

(vi) All poor people in Mumbai.

"Poor" is a relative term unless a specific economic threshold (like a poverty line) is provided.

∴ It is not a set.

(vii) All boys in your class weighing less than 50 kg.

Weight is a measurable, objective quantity.

∴ It is a set.

(viii) All persons of repute in your colony.

"Repute" (reputation) is based on personal opinion and varies from person to person.

∴ It is not a set.

(ix) All even numbers greater than 100.

The criteria for being even and being greater than 100 are mathematically definite.

∴ It is a set.

(x) All integers less than -5.

Integers less than -5 (such as -6, -7, …..) are clearly defined.

∴ It is a set.