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1. Your task

Do Exercises 7.1.44, 7.3.8, 7.5.6, and 8.2.24, plus Supplementary Exercise 7.38 (on page 535) from RosenBook.

2. Clarifications

For Exercise 7.1.44 parts (a) and (b), replace S with R, where R is one of the relations you are counting. So part (a) asks to count how many relations contain (a,b), and part (b) asks to count how may relations do not contain (a,b).
Supplementary Exercise 7.38 should read "..., where C and D are equivalence classes of R∩R^-1, ..."