Question

The set of intelligent students in a class is
(a) A finite set
(b) A null set
(c) Not a well-defined collection
(d) A singleton set

Answer 1

Hint: Think of the basic definition of the types of sets given in the question. Focus on the point that the definition of an intelligent student may vary from person to person, so the set of intelligent students will also vary from person to person and his perception.

Complete step-by-step answer:
The set given to us is a set of all the intelligent students in a class. We know that we cannot measure the intelligence of a student in a scale and compare, but intelligence is an abstract quantity and the definition of intelligence may vary from person to person.
Now, if we talk about the types of sets given in the option. A finite set is a set which has the number of elements defined and finite. So, the set of intelligent students is not a finite set as the number of elements may vary in the set from person to person.
Next, if we talk about the null set, it is defined as a set which has no elements, i.e., the number of elements is 0, but the set of intelligent students may or may not contain students, so it is not always a null set.
The set of intelligent students is not a singleton set as well, because the set which contains only one element is termed as singleton and the set of intelligent students not necessarily contains one student.
However, as the number of students are varying with the perceptions of person to person, so the set of the intelligent students will be categorised as not a well-defined collection.
So, the correct answer is “Option C”.

Note: At the first glance at the question, you might think that the answer would be a finite set, but the main point to be thought over that out of a bunch of students, if you think two are intelligent it doesn’t mean that someone else would think the same, they may find 3 students to be intelligent, as the barometer for intelligence may differ from person to person.