__Partition on Set A__

It is defined to be a set of non-empty subsets A_{i}, which are pairwise disjoint as there is no intersection and whose union yields to original set A. This means that the two condition that are to be satisfied are:

Partition on Set A is indicated as given below:

__Covering on Set A__

It is defined as a set on non-empty subsets A_{i}, whose union leads to the original set A and which are need not be pairwise disjoint. Here are the two conditions that are to be satisfied:

__Rule of Addition__

Given partition on ‘A’ be A_{i} where i = 1, 2, 3,………,n

__Rule of Inclusion & Exclusion__

Rule of addition is not applicable on the covering on Set A since the individual subsets are not disjoint. In such a case this Rule of Inclusion & Exclusion is applied. Therefore by generalizing above form we get: