اشتراک (نظریه مجموعه‌ها)

${\displaystyle \bigcap S:=\bigcap _{A\in S}A:=\{y\in X:\forall A\in S,y\in A\}}$

${\displaystyle A_{1}\cap A_{2}\cap \cdots A_{n}=(A_{1}\cap A_{2}\cap \cdots A_{n-1})\cap A_{n}}$

${\displaystyle A\cap A=A}$

${\displaystyle A\cap B=B\cap A}$

${\displaystyle A\cap \phi =\phi \cap A=\phi }$

${\displaystyle (A\cap B)\cap C=A\cap (B\cap C)}$

${\displaystyle A\cap (B\cup C)=(A\cap B)\cup (A\cap C)}$

${\displaystyle A\cup (B\cap C)=(A\cup B)\cap (A\cup C)}$

${\displaystyle A\subseteq B}$ اگر و تنها اگر ${\displaystyle A\cap B=A}$.