Question

Observe the following sets and answer the question given below.
A = The set of all residents in Mumbai.
B = The set of all residents in Bhopal.
C = The set of all residents in Maharashtra.
D = The set of all residents in India.
E = The set of all residents in Madhya-Pradesh.
Which set can be chosen as the suitably as the universal set
A) Set A
B) Set B
C) Set C
D) Set D

Answer 1

To answer this question first we need to understand the meaning of sets, subsets and universal sets. If we know the basic difference between sets, subsets and universal sets, then we can give the answer to this question very easily. Observe the sets, they consist of names of states and countries. So, use the knowledge of this and choose the right answer.

Complete step by step answer:
A set is a well-defined collection of elements.
Example- Consider the set X= set of all students in your school, set Y= set of all the students in your class.
We note that every element of Y is also an element of X, we say that Y is a subset of X.
Universal set- Usually, in a particular context we have to deal with the elements and subsets of a basic set which is relevant to that particular context.
For example, while studying the system of numbers we are interested in natural numbers and its subset such as the set of prime numbers, the set of even numbers and so forth. This basic set is known as ‘Universal set’.
So, in this question we have to identify the universal set.
We know that Bhopal and Mumbai are cities, and they are located within Maharashtra and Madhya Pradesh respectively. So residents in Mumbai is the subset of residents in Maharashtra. Similarly, residents in Bhopal are the subset of residents in Madhya Pradesh. Now Madhya Pradesh and Maharashtra are states of India, i.e., they lie in the country.
Therefore, residents in Maharashtra and residents in Madhya Pradesh both are subsets of residents in India.
Hence, we can say that from all the above sets, “residents in India” is the universal set.

So, the correct answer is “Option D”.

Note: The above question has low chances of mistakes, but if someone doesn't have the basic knowledge of sets, subsets and universal sets, then the person may face problems in answering the question, or may fail to answer. Here, one must know about the difference between cities, states and countries in terms of sets, subsets and universal sets. The options and sets are all similar, so choose the right option carefully.