Observe the following sets and answer he quesions given below.
A = The set of all residens in Mumbai.
B = he set of all residens in Bhopal.
C = he sets of all residents in Maharashtra.
D = The sets of all residents in India.
E = The sets of all residents in Madhya-Pradesh.
(i)Write the subset relation between the sets A and C.
(ii)Write the subset relaion between the sets E and D.
(iii)Which set can be chosen suitably as the universal set?
gsjvsdk
To answer the questions, we need to understand the concept of subset and universal set.
1. Subset relation between sets A and C:
A subset B is a set in which all the elements of set A are also present in set B. In other words, every element of A is also an element of B.
In this case, since A represents the set of residents in Mumbai and C represents the set of residents in Maharashtra, we can say that A is a subset of C, denoted as A ⊆ C. This is because every resident in Mumbai is also a resident of Maharashtra.
2. Subset relation between sets E and D:
Similar to the previous case, E is the set of residents in Madhya Pradesh and D is the set of residents in India. We can determine the subset relation by checking if every resident in Madhya Pradesh is also a resident of India. Since every resident in Madhya Pradesh is a resident of India, we can say that E is a subset of D, denoted as E ⊆ D.
3. A suitable universal set:
A universal set is a set that contains all the possible elements under consideration. In this case, since we are dealing with the sets of residents in different geographical locations, the most suitable universal set would be the set of all residents in the entire country. Thus, the set D (the set of residents in India) can be chosen as the universal set.
So, the answers to the questions are:
(i) A ⊆ C
(ii) E ⊆ D
(iii) The set D (The set of residents in India) can be chosen as the universal set.