Final answer:
The statement that a set containing no elements is called the empty set or null set, represented by {} or Ø, is true. The empty set plays a significant role in set theory and operations such as union and intersection.
Step-by-step explanation:
It is true that a set that contains no elements is called the empty set or null set, and is represented by {} or Ø. An empty set is a fundamental concept in set theory, a branch of mathematical logic that studies collections of objects. The empty set is the unique set having no elements; its size or cardinality is zero.
In mathematics, the notion of nothingness or emptiness is visualized through the concept of the empty set. The comparison to the number zero in the domain of algebra, specifically vector algebra, shows the empty set as the null vector, which is a vector of all zero components, indicating no length and no direction. This analogy helps in understanding the importance of nothingness in various branches of mathematics. Moreover, the concept of a system, as outlined in Essential Knowledge 1.A.1, denotes objects with no internal structure, which can be related back to the property of the empty set containing no elements.
Furthermore, when discussing set operations like intersection (AND) and union (OR), the empty set plays a critical role. For example, if the intersection of two sets contains no common elements, their intersection is the empty set. Conversely, the union of any set with the empty set will simply be the original set since the empty set adds no elements to the union.
The correct option for the given statement is a. True.