1. The problem is to understand the concept of a universal set in set theory. 2. A universal set, often denoted by $U$, is the set that contains all the objects or elements under consideration for a particular discussion or problem. 3. Every other set in that context is a subset of the universal set. For example, if we are discussing sets of natural numbers, the universal set might be $U = \{1, 2, 3, \ldots\}$. 4. The universal set is important because it defines the 'universe' of discourse and helps in defining complements of sets. The complement of a set $A$ is the set of all elements in $U$ that are not in $A$, denoted $A^c = U \setminus A$. 5. In summary, the universal set is the 'biggest' set containing all elements relevant to the problem, and it is fundamental in operations like union, intersection, and complement.