Question

4. Consider the sets A= {1,2,3,..., 365} , B = {Jan., Feb. , ... , Dec.} , C = {1,2,3,..., 31} and the function f: A+BxC, defined by f(x) = (month for day r , day of the month for day ), in a regular year (not leap year). For example: f (365)=(Dec. , 31), since the date of the last day of the year is December 31st. (a) What is f(1), f(32), and f(359) ? (b) Is f injective? Explain. (c) Is f surjective? Explain.