Partition and Covering on Set A

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: