Subsets of a Set2

Write all subsets of the set $B$, given $B = \{ 1, 2, \emptyset \}$.

In this problem, you are asked to find all the subsets of a given set. Understanding how to work with subsets is a fundamental concept in set theory, which is a foundational aspect of mathematical logic and analysis. A subset is essentially any combination of elements from the original set, including the possibility of not choosing any elements at all, which results in the empty set. Furthermore, the set itself is also considered one of its subsets.

The task involves recognizing that the number of subsets of a set with '$n$' elements is given by $2^n$. This is because each element can either be included or not included in a subset, leading to two choices per element. For the set $B = \{1, 2, \emptyset\}$, which has 3 elements, this means there should be $2^3 = 8$ subsets in total.

This problem introduces you to the power set, which is the set of all subsets of a given set. The concept of power sets is crucial when dealing with functions and relations, as well as forming the base for more advanced topics such as product topology and cardinality. Solving problems like this helps you understand how to enumerate and work with different combinations of elements, a skill that is pertinent in both theoretical and applied mathematics.