Intersection

An intersection is the set of elements common to every set in a given collection. For sets $A,B$,

More generally, for an indexed family of sets $(A_i)_{i\in I}$,

Intersection is dual to union and is closely related to containment : one has $A\subseteq B$ exactly when $A\cap B=A$.

Examples:

• $\{1,2\}\cap\{2,3\}=\{2\}$.
• If $A=\{x\in\mathbb{R}: x<0\}$ and $B=\{x\in\mathbb{R}: x\ge 0\}$, then $A\cap B=\varnothing$ (see empty set ).