We define six binary relations on the power set of an n-element set and describe their basic structure and interrelationships. An auxiliary relation is noted that will assist in determining the cardinalities of each. We also indicate an eighth relation that may be of interest. We conclude the first section by computing several quantities related to walks in the graph of the sixth relation. In the second section we turn our attention to the basic structure and cardinalities of the auxiliary relation noted in section one and several additional relations. We also compute seven sums associated with these relations and indicate connections four relations have with Wieder's conjoint and disjoint k-combinations.