1) Let S be the set of all UT CPEN students and C the set of all courses offered in Department of Computer Engineering for spring 2011. a) Forx Sandy EC, we say y = f(x) if and only if student x has registered course y. Does f: S→C define a function? Why or why not? b) Forx eS and y = P (Peis the power set of C), we say y = f(x) if and only if student x has registered every course in set y. Does f: SP define a function? Why or why not? c) For x ЄS and y = P (Pis the power set of C), we say y = f(x) if and only if student x has registered for every course in set y and for no course in set C-y. Does f: S→ Pc define a function? Why or why not?