Let R be an equivalence relation on a non-empty set A. Denote by [a] the equivalence class of an element a∈A.
a. (i) State the property that describes the relationship between any two equivalence classes of R.
b. (ii) Prove that, for any a,b∈A, either [a]=[b] or [a]∩[b]=∅.
c. (iii) Explain briefly how this property ensures that the collection of all equivalence classes forms a partition of A.