Write definitions for the following:

a. ExhaustivePartDecomposition

b. PartPartition

c. PartwiseDisjoint

These should be analogous to the definitions for ExhaustiveDecomposition, Partition, and Disjoint . Is it the case that PartPartition(s, BunchOf (s))? If so, prove it; if not, give a counterexample and define sufficient conditions under which it does hold.