Let U denote the set of all points in and on the unit square shown in Fig. 7.29. That is, U = {(x, y) | 0 ‰¤ x ‰¤ 1, 0 ‰¤ y ‰¤ 1}. Define the relation R on U by (a, b) R (c, d) if (1) (a, b) = (c, d), or (2) b = d and a = 0 and c = 1, or (3)b = d and a = 1 and c = 0.

(a) List the ordered pairs in the equivalence classes [(0.3, 0.7)], [(0.5, 0)], [(0.4, 1)], [(0, 0.6)], [(1, 0.2)]. For 0 ‰¤ a ‰¤ l, 0 ‰¤ b ‰¤ l, how many ordered pairs are in [(a, b)]?
(b) If we "glue together" the ordered pairs in each equivalence class, what type of surface comes about?

Transcribed Image Text:

1,1 (0, 0) Figure 7.29