Question

Observe the following sets and answer the questions given below.
A = The sets of all residents in Mumbai.
B = The set of all residents in Bhopal.
C = The set of all residents in Maharastra
D = The set of all residents in India.
E = The set of all residents in Madhya-Pradesh

(i) Write the subset relation between the sets A and C.
(ii) Write the subset relation between the sets E and D.
(iii) Which set can be chosen suitably as the universal set?

Answer 1

(i) A = set of all residents in Mumbai
C = set of all residents in Maharashtra
We know that Mumbai is the capital of Maharashtra.
i.e., A is contained in C.
Hence, A$\subset$C

(ii) D = set of all residents in India
E = set of all residents in Madhya Pradesh.
We know that Madhya Pradesh is one of the states of India.
Hence, E$\subset$D

(iii) Set D can be considered a universal set, because all the other sets are either states or cities of India.
i.e., all the other sets are contained in set D.
Hence, D is a universal set.