Which of these are recursive definitions that correctly define f(n) = n! for all natural numbers n? hint: proofread them carefully. you're looking for serious structural problems, e. g. the equations don't define the right value (or any value) for some of the possible inputs. you're not looking for subtle style issues. select one or more: a. f(0) = 1, f(1) = 1, f(n) = n. f(n − 1) for n > 2 b. f(0) = 1, f(n) = n. f(n − 1) for n > 1 cf(0) = 1, f(n) = n · f(n) for n > 1 d. f(0) = 1, f(1) = 1, f(n) = f(n − 1). f(n - 2) e. f(1) = 1, f(n) = n. f(n − 1) for n > 2 f. f(0) = 1, f(n) = n · (n − 1) · (n − 2) 2.1 0 g. f(0) = 1, f(n + 1) = (n +1). f(n) for n > 1 h . f(0) = 1, f(n + 1) = (n + 1). f(n) for n > 0