How is the complement of set A defined?

The complement of set A is defined as the set of all elements in the universal set that are not in A. This encompasses every element that falls outside of set A, effectively representing everything available within the context of a given universal set, apart from those elements specified in A.

The universal set serves as the overarching set that includes all possible elements relevant to a particular discussion or problem. By identifying elements that are not part of A, the complement provides a complete view of the remaining options within the universal set. This concept is crucial in set theory and helps in various areas of mathematics, especially when dealing with probabilities and logical operations.

In contrast, the other options describe different set relationships or concepts that do not align with the definition of a complement. For instance, options referring to elements within A, or those pertaining to interactions between A and another set, do not accurately capture the exclusivity of the complement. The complement focuses solely on the distinction of elements outside of set A, making option B the precise and correct definition.