Let Z be the set of all integers. A relation R on Z is defined by
aRb⟺a−b is divisible by 6.
Answer the following:
a. (i) Prove that R is an equivalence relation on Z.
b. (ii) List all distinct equivalence classes of R, using the least non-negative integer in each class as its representative.
c. (iii) Identify the equivalence class that contains −15.