Exercise 3.7.3: Partial orders on complex relations. About Suppose R1 is a relation on domain X1 and R2 is a relation on domain X2 Define a new relation R whose domain is X1 X X2: (21, 22) R(acj , 2'2 ) if a1 Ria, and 2 R2 2'2 (a) Show that if R1 and R2 are both partial orders, then R is also a partial order. (b) Now change the relation R so that (21, 2) R(x4, 2'2 ) if x1 Rix, OR x2 R2x2. Give an example in which R1 and R2 are partial orders but R is not a partial order. Feedback