QUESTION 1 (7 points). Let f:Z\times Z->Z\times Z be defined as f(a,b)=(a-b,a-3b).
(1) Show that f is injective.
(2) Show that if (x,y) is in the range of f, then x-y is even.
(3) Show that f is not surjective. Hint: use part (2) to find a counterexample.