Disjoint Sets

Two sets $A$ and $B$ are called disjoint if they share no elements at all — that is, their intersection is empty:

For example, $A = \{1,3,5,7\}$ (odd numbers) and $B = \{2,4,6,8\}$ (even numbers) are disjoint, since no number is both odd and even: $A \cap B = \emptyset$. On the other hand, $A = \{1,3,5,7\}$ and $C = \{5, 10, 15\}$ are not disjoint, because $5$ belongs to both: $A \cap C = \{5\} \ne \emptyset$. …