Symmetric closure
In mathematics, the symmetric closure of a binary relation R {\displaystyle R} on a set X {\displaystyle X} is the smallest symmetric relation on X {\displaystyle X} that contains R . {\displaystyle R.} For example, if X {\displaystyle X} is a set of airports and x R y {\displaystyle xRy} means "there is a direct flight from airport x {\displaystyle x} to airport y {\displaystyle y} ", then the symmetric closure of R {\displaystyle R} is the relation "there is a direct flight either from x {\displaystyle x} to y {\displaystyle y} or from y {\displaystyle y} to x {\displaystyle x} ".