Closure

Closure is a relation created from adding elements to a relation so that it has one of the following three traits


 * 1) Reflexive relation
 * 2) Symmetric
 * 3) Transitive

You are adding the minimum amount of ordered pairs necessary for the trait being added.

There is no antisymmetric closure for two reasons:
 * 1) you cannot add elements to give the property, you have to take out elements
 * 2) there are multiple ways you can take out elements to induce the property. So no single one like there are closures for the three other properties