I think your R2 relationship is wrong or wrong in the book, because if you list R 1 and R2, you won't get that result at all.

If R2 is changed to {(a, d), (c, b), (d, c)}, then the calculation result is correct.

R 1 R2: (a, a)-(a, d) can compound (a, d).

(a, c)-(c, b) can be compounded into (a, b).

(b, d)-(d, c) can be compounded with (b, c).

So r 1 R2 = {(a, d), (a, b), (b, c)}.

R2 R 1: from R2 to R 1 there is only (c, b)-(b, d), so only (c, d) can be obtained.