Partition and Covering on Set A

Partition on Set A

It is defined to be a set of non-empty subsets Ai, 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 conditions

Partition on Set A is indicated as given below:

Partiton on Set A indication

Covering on Set A

It is defined as a set on non-empty subsets Ai, 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:

Covering on set A conditions

Rule of Addition

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

Rule of Addition on Set A

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:

Rule of Inclusion & Exclusion on Set A
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