please also include explanations

5. [6 Points] Properties of functions (additional exercise 4.3.1). Consider the following func- tions from Z x Z to Z. Which ones are surjective? Justify your answer. (a) may) =2m-4y (13) Hay) = |$| - |y| (C) f(w,y)=:v+y2 6. [8 Points] Properties of functions (additional exercise 4.3.4). Let 3,, denote the set of binary strings1 of length n. For each of the functions below, indicate whether the function is injective, surjective, neither, or both (a bijection). If the function is not injective or not surjective, give an example showing why. (a) f : B4 > 83. The output of f is obtained by taking the input string and dropping the rst bit. For example, f(1011) = 011. (b) f : 83 > 33. The output of f is obtained by taking the input string and replacing the rst bit by 1, regardless of whether the rst bit is a 0 or a 1. For example, f(001) = 101 and f(110) = 110