Disjoint Sets

Definition 1. Two sets $X$ and $Y$ are disjoint if

\[X \cap Y = \empt.\]

A set $X$ is disjoint if the elements of $X$ are pairwise disjoint, i.e.

\[\forall A, B \in X :\enspace A \neq B \,\rimp\, A \cap B = \empt.\]

Not disjoint sets are called joint.

Proposition 1. $\empt$ is the only self-disjoint set.

Proposition 2. $\empt$ is the only set disjoint to every other set.