Represent the following seven sentences using and extending the representations developed in the chapter:

a. Water is a liquid between 0 and 100 degrees.

b. Water boils at 100 degrees.

c. The water in John’s water bottle is frozen.

d. Perrier is a kind of water.

e. John has Perrier in his water bottle.

f. All liquids have a freezing point.

g. A liter of water weighs more than a liter of alcohol.

1 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.