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

A. (i), (ii), (iv) only.
B. (i), (iv), (v) only.
C. (ii), (iii), (v) only.
D. (iii), (iv) only.

Answer 1

Hint: We first try to define the definition of set. Then we find if the given options are qualitative or quantitative. Then we try to form the set of the given options.

Complete step by step answer:
Any kind of set has elements which have characteristics of quantity not quality. Quality can’t be classified in a set. The elements of the set also have to satisfy the conditions of the set.
Now we take each and every given condition and try to make a set
For the collection of prime numbers, we have numbers which are only divisible by 1 and that number itself. This is obviously a quantitative set and also can be made in a set.
For the collection of easy sub topics in this chapter, we have chapters which have to be easy subtopics. A thing being easy or tough is a subjective and qualitative thing. This is obviously quantitative and also can’t be made in a set.
For the collection of good teachers in your school, we have teachers who have to be good. A person being good or bad is a subjective and qualitative thing. This is obviously quantitative and also can’t be made in a set.
For the collection of girls in your class, we have the girls in the class. We are arranging their names as the input of the collection. This is obviously a set.
the collection of odd natural numbers, we have numbers which are not divisible by 2 and that number is a natural number. This is obviously a quantitative set and also can be made in a set.

So, the correct answer is “Option B”.

Note: We first think that collection of girls in your class can’t be quantified as a fixed characterisation is not given. But we are just taking some people who are countable and featured as a girl in the class. Also, we need to remember that the other two sets are infinite sets.