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Tim Ratigan gives the formal definition of disjoint.

We say that a family (we use family as the collective noun for sets) of sets is pairwise disjoint if every two are disjoint.

Two sets $A$ and $B$ are disjoint if and only if $A\cap B=\emptyset$, where $\emptyset$ denotes the empty set $\{\}$.

That is, there is no element $a$ that is both part of $A$ and $B$. In a Venn diagram of the sets $A$ and $B$, there would be no overlap between the two sets.