Sure! Here are the answers to the questions provided:
(i) To find the number of subsets of a set with 'n' elements, you can use the formula 2^n. In this case, the set F = {mango, apple} has 2 elements. Therefore, the number of subsets of set F can be calculated as 2^2 = 4.
(ii) The possible subsets of set F are:
1. Empty set {}
2. {mango}
3. {apple}
4. {mango, apple}
(iii) Among these subsets, the improper subset is the subset that doesn't include all the elements of the original set. In this case, the improper subset is the empty set {}. This subset is improper because it doesn't contain either 'mango' or 'apple', which are the elements of set F.
Additionally, for set X = {b, a, l} being a set of letters of the word 'BALL', we have the following subsets:
1. Empty set {}
2. {b}
3. {a}
4. {l}
5. {b, a}
6. {b, l}
7. {a, l}
8. {b, a, l}
These subsets follow the concept of subsets, including the empty set and the set itself as subsets.
