8. a) The relation R contains 34 ordered pairs.
R = { (1,1), (4, 4), (7, 7), (10, 10), (1, 4), (4, 1), (1, 7),
(7, 1), (1, 10), (10, 1), (4, 7), (7, 4), (4, 10), (10, 4), (7, 10), (10, 7),
(2, 2), (5, 5), (8, 8), (2, 5), (5, 2), (2, 8), (8, 2), (5, 8), (8, 5),
(3, 3), (6, 6), (9, 9), (3, 6), (6, 3), (3, 9), (9, 3), (6, 9), (9, 6) }
Notice that the ordered pairs can be grouped into three parts, elements 1, 4, 7 and 10 occur together in all possible combinations, elements 2, 5 and 8 occur together in all possible combinations and element 3, 6 and 9 occur together in all possible combinations. This idea will be explored in more detail in the later sections of chapter 10.
b) R-1 = { (1,1), (4, 4), (7, 7), (10, 10), (4, 1),
(1, 4), (7, 1), (1, 7), (10, 1), (1, 10), (7, 4), (4, 7), (10, 4), (4, 10), (10, 7), (7,
10),
(2, 2), (5, 5), (8, 8), (5, 2), (2, 5), (8, 2), (2, 8), (8, 5), (5, 8),
(3, 3), (6, 6), (9, 9), (6, 3), (3, 6), (9, 3), (3, 9), (9, 6), (6, 9) }
YES R = R-1.