Question

Which of the following collections are sets?
(i) The collection of prime numbers
(ii) The collection of easy sub topics in this chapter.
(iii) The collection of good teachers in your school.
(iv) The collection of girls in your class.
(v) The collection of odd natural numbers.

Answer 1

A well defined collection of objects is called a set.

(i) The collection of prime numbers is a set, because it includes a well defined collection of numbers which are not divisible by any number except 1 and itself.

(ii) The collection of easy sub-topics in this chapter is not a set, because it might be easy for one student and difficult for another. As it is not a well defined collection, it is not a set .

(iii) The collection of good teachers in school is not a set, because we do not know in which sense are they good. They might be good in music, drawing or any field. As it is not a well defined collection, it is not a set.

(iv) The collection of girls in a class is a set, because it is a well defined collection.

(v) The collection of odd natural numbers is a set, because it includes a well defined collection of natural numbers which are not divisible by 2.