4. Let A = {0, c, e, a, n} and B = {n, i, g, h,...

 

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4. Let A = {0, c, e, a, n} and B = {n, i, g, h, t}. Using A as the domain and B as the co-domain, define functions having the following properties and explain why the properties hold, or explain why it is impossible to have such a function. To define a function f(x), specify the images for each of the five elements of the domain using the form f(a) = B. a. A function that is neither injective nor surjective. (Equivalently, a function that is not injective and is also not surjective) b. A function that is surjective but not injective. c. A function that is injective but not surjective. 4. Let A = {0, c, e, a, n} and B = {n, i, g, h, t}. Using A as the domain and B as the co-domain, define functions having the following properties and explain why the properties hold, or explain why it is impossible to have such a function. To define a function f(x), specify the images for each of the five elements of the domain using the form f(a) = B. a. A function that is neither injective nor surjective. (Equivalently, a function that is not injective and is also not surjective) b. A function that is surjective but not injective. c. A function that is injective but not surjective.