Disjoint sets

Definition

Let $A$ and $B$ be sets. The sets $A$ and $B$ are disjoint when $A \cap B = \varnothing$. A family of sets $(A_i)_{i \in I}$ is pairwise disjoint when $A_i \cap A_j = \varnothing$ for all $i, j \in I$ with $i \neq j$.

Remarks

Example: $\{1, 2\}$ and $\{3, 4\}$ are disjoint, but $\{1, 2\}$ and $\{2, 3\}$ are not. The blocks of a partition are pairwise disjoint. For finite disjoint sets, the number of elements of $A \cup B$ is the sum of the numbers of elements of $A$ and $B$.

Explanations

L1 human

Disjoint sets do not overlap. The even integers and the odd integers are disjoint, because no integer is both.