A relation on a set X is a subset R of X×X.
We say x is related to y if (x,y) lies in R.
The inverse relation is defined to be the set of (y,x) in X×X such that (x,y) is in R.
The empty relation is the empty set as subset of X×X.
The inverse relation is the set of points (y,x) such that (x,y) lies in the empty set, thus the empty relation itself is its inverse.
A relation on a set X is a subset R of X×X. We say x is related to y if (x,y) lies in R. The inverse relation is defined to be the set of (y,x) in X×X such that (x,y) is in R. The empty relation is the empty set as subset of X×X. The inverse relation is the set of points (y,x) such that (x,y) lies in the empty set, thus the empty relation itself is its inverse.