Set operation (Boolean) in the context of Binary relation

In set theory, the intersection of two sets ${\displaystyle A}$ and ${\displaystyle B,}$ denoted by ${\displaystyle A\cap B,}$ is the set containing all elements of ${\displaystyle A}$ that also belong to ${\displaystyle B}$ or equivalently, all elements of ${\displaystyle B}$ that also belong to ${\displaystyle A.}$ The notion of intersection as an algebraic operation with sets as operands has been generalized from geometry, where it is encountered in the case of geometric sets of points, such as individual points, lines (infinite uncountable sets of points), planes, etc.