What does it mean for two sets to be disjoint?

• A. They have at least one element in common
• B. They are equal
• C. They have no elements in common
• D. They contain the same number of elements

Answer: (C)

Two sets are considered disjoint when they have no elements in common. This means that if you were to list the elements of both sets, there would not be any overlap; in other words, the intersection of the two sets is empty. Understanding disjoint sets is important in various fields, including probability and statistics, because it helps in determining events that do not share outcomes.

The concept of disjoint sets is fundamental in set theory; for example, the sets of even numbers and odd numbers are disjoint because no number can be both even and odd. In contrast, situations where sets do share elements or have the same number of elements are not classified as disjoint, providing a clear distinction in their definitions and characteristics.