Solutions to selected exercises of Chapters 17 and 18 Bas Luttik

The proofs below are given in textual form and contain the minimum amount of detail both with respect to the logic and reasoning involved, and with respect to the properties and definitions pertaining to sets, relations and mappings. Note that most applications of logical reasoning steps (i.e., the introduction and elimination rules discussed in Parts I and II of the book) are left implicit, but you should nevertheless be able to recognise where and how they are applied. For your convenience, there is also an appendix at the end of this document with very detailed logical derivations, following the methods of Parts I and II to the letter and being explicit about which rule is applied when. We encourage you to compare the proofs in textual form and the logical derivations, to make sure that you understand every step. At examinations you may give proofs about properties of sets, relations an mappings either in textual form, or as logical derivations.