Write definitions for the following:
1. ${ExhaustivePartDecomposition}$
2. ${PartPartition}$
3. ${PartwiseDisjoint}$
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.
1. ${ExhaustivePartDecomposition}$
2. ${PartPartition}$
3. ${PartwiseDisjoint}$
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.
Write definitions for the following:
1. ${ExhaustivePartDecomposition}$
2. ${PartPartition}$
3. ${PartwiseDisjoint}$
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.