Conditions for the partition sub-sets to be an equivalence relation:
(i) The partition sub-sets must be disjoint i.e.their is no common elements between them
(ii) Their union must be equal to the main set (super-set)
Here the set A={1,2,3,4,5,6},the partition sub-sets {1,3},{2,4,5},{6} are pairwise disjoint and their union i.e. {1,3} U {2,4,5} U {6} = {1,2,3,4,5,6} = A,which is the condition for the partition sub-sets to be an equivalence relation of the set A.
Let and x, y R} be a relation in R. The relation R is
The number of onto functions that can be defined from a finite set A containing n elements onto a finite set B containing 2 elements == .