Intersects

Intersecting and disjoint sets

We say that ${\displaystyle A}$ intersects (meets) ${\displaystyle B}$ if there exists some ${\displaystyle x}$ that is an element of both ${\displaystyle A}$ and ${\displaystyle B,}$ in which case we also say that ${\displaystyle A}$ intersects (meets) ${\displaystyle B}$at${\displaystyle x}$. Equivalently, ${\displaystyle A}$ intersects ${\displaystyle B}$ if their intersection ${\displaystyle A\cap B}$ is an inhabited set, meaning that there exists some ${\displaystyle x}$ such that ${\displaystyle x\in A\cap B.}$