Disjointwith

Disjointwith is a term used in mathematics, particularly in set theory, to describe the relationship between two sets. Two sets are considered disjoint with each other if they have no elements in common. In other words, their intersection is the empty set. This means that there is no element that is a member of both sets simultaneously.

The concept of disjoint sets is fundamental in various areas of mathematics. For instance, in number theory, the set of even numbers and the set of odd numbers are disjoint with each other. Similarly, in probability theory, mutually exclusive events are those whose corresponding outcomes form disjoint sets.

Formally, for two sets A and B, they are disjoint with each other if and only if A ∩ B = ∅, where ∩ denotes the intersection operation and ∅ denotes the empty set. This property is symmetric, meaning if set A is disjoint with set B, then set B is also disjoint with set A. The term "disjoint with" emphasizes this mutual lack of shared elements between two distinct sets.