Let f: A→B and g:B→C be maps.
(A) If f and g are both one-to-one
functions, show that g∘f is one-to-one.
(B) If g∘f is onto, show that g is
onto.
(C) If g∘f is one-to-one, show that f
is one-to-one.
(D) If g∘f is one-to-one and f is onto,
show that g is one-to-one.
(E) If g∘f is onto and g is one-to-one,
show that f is onto.
(Abstract Algebra)