®
Equivalence class [a] containing a ∈ X for an equivalence relation R in X is
the subset of X containing all elements b related to a ®
A function f : X → Y is one-one (or injective) if
f (x1) = f(x2) ⇒ x1 = x2 ∀  x1, x2 ∈ X ®
A function f : X → Y is onto (or surjective) if given any y ∈ Y, ∃ x ∈ X such
that f (x) = y ®
A function f : X → Y is one-one and onto (or bijective), if f is both one-one
and onto