Let R be the relation defined on the set of eight-bits strings by s1RS2
provided that s1 and s2 have the same number of zeros.
(a) Show that r is an equivalent relation.
(b) How many equivalence classes are there?
(c) List one member of each equivalence class.
The following remark is probably not very suitable to the level of the question, but if there is some function f : X -> Y, then the relation x₁ R x₂ defined by f(x₁) = f(x₂) is an equivalence relation. It is important that f is a function, not a general relation.