Problem 3. For each of the following functions, determine whether it is injective / surjective / bijective. If any of these properties is not fulfilled, give an explanation. (a) f : Z- Z, f(m) = m -12 [2 points] (b) f : Z - Z, f(m) = m> + 1 [2 points] ( c) f : Z xZ -+ Z, f(m, n) = m+n [2 points] (d) f : Z x Z - Z, f(m, n) = n3 +m [2 points] (e) f : Z x Z -+ Z, f(m, n) =m [2 points] Problem 4. Let A, B, C be arbitrary sets. Prove or disprove: If there is a bijection f : A -> B and there is a bijection g : A -> C, then there is a bijection h : B - C. [4 points] Problem 5. Let A be any set. Prove the following statement: If A is finite, then A has no proper subset B C A for which a bijection f : B - A exists. [3 points] Problem 6. Prove the following statement: Z has a proper subset A C Z for which a bijection f : Z - A exists. [3 points]