The data in the information system can be used to discern classes only to a certain degree. Not all attributes may be required in order to be able to do so, however. This is why the next definition is helpful.
What this implies is that a relative reduct contains enough information to discern objects in one class from all the other classes in the information system.
To find the relative reducts for our example, the discernibility functions are employed. Each function is minimized to a sum of products form, as shown below.
¯
= studies
This gives the desired relative reducts. For instance, RED() = {\studies, education}, {studies, works}\.The relative reducts are minimal, because each discernibility function was minimized. A minimal (relative) reduct is thus a reduct in which none of the attributes may be removed without removing the reduct property.