Question

Show that relation R defined on S :?
(i) Show that relation R defined on the set S = {1,2,3,...,16} as R = {(m, n) ∈ S × S : m = 2^k n for some integer k}
is an equivalence relation. (ii) Into how many distinct equivalence classes does this relation R partition the set S? (iii) Determine the equivalence class of the element 2.