In this chapter, the author proceeds to apply his system to logical relations which were not considered by Aristotelian logic. These includes logical relations between multiply quantified sentences; logical relations between propositional combinations of quantified sentences; and some logical relations between relations. Transposition was formulated above for predicates with singular definite noun phrases as subjects. Instead of proving the generalized form of Transposition for any predicate, which would require using complex symbols and indices, the chapter proves it for two examples, one with 'every' as quantifier, the other with 'some'. The chapter examines how the semantic principles developed in this work should be applied to the analysis of identity, and how identity should be incorporated in the deductive system.