9.41. a. Prove that the intersection of two equivalence relations on a nonempty set is an equivalence relation. b. Consider the equivalence relations R2 and R3 defined on Z by a R2 b if a = b (mod 2)...

41

Extracted text: 9.41. a. Prove that the intersection of two equivalence relations on a nonempty set is an equivalence relation. b. Consider the equivalence relations R2 and R3 defined on Z by a R2 b if a = b (mod 2) and a R3 if a = b (mod 3). By (a), R1 = R2 N R3 is an equivalence relation on Z. Determine the distinct equivalence classes in R1. |