11. Suppose you are the teacher of this course and you are grading exams. You have asked students to complete the definition: Let f : A - B be a function. We say that f is injective if . ... Most of your students exactly quote one of the properties in the definition, and you give them full credit. However, a few students write down something else and you have to figure out what to do. For each of the following sample answers, try to characterize the student's response. You might use characterizations like "Absolutely correct," "The student has 'injective' confused with another concept," "The student has the right idea but what is written is incomplete or flawed," "The student is writing a fact about injective functions but not the definition," "The statement is comprehensible but false," or "The student's response is not comprehensible." Briefly explain your answer. (a) For all be B, If [(bill = 1. (b) For every y there's at most one x. (c) For every x there's at most one y. (d) If an # a2, then f(a) # f(a2). (e) For all an , az e A, if f(al) = f(a2), then al = a2. (f) Every line hits the graph at most once. (g) Every vertical line hits the graph at most once. (h) Every horizontal line hits the graph at least once. (i) Two things in the domain can't go to the same point in the codomain. (j) If f(A) = B then f(a) = f(b), ab. (k) Two arrows can't end at the same point. (1) If an = az then f(a ) = f(az)