👉 In mathematics, a "preclosed" relation (or simply closed) on a set X is a relation that has no elements in common with any other relation defined on X. This means that if you have two relations R and S defined on X, then R ∩ S = φ where φ is the empty set. For example, consider the set X = {1, 2, 3}, let's define a relation R over X as follows: R = {(x, y)