For True/False statements: a) State either the statement is True or False. b) Justify your answer by giving a proof or a counterexample. 1. True/False: If u is harmonic and u > -1 on C, then u is a constant function. 2. Find all entire functions f such that e4 (f(z) + sin(32) + 2) > 1 for all z E C. 3. True/False: If f is entire and |f(z)| < 1+|2| for all z E C, then f is a constant multiple of 1+z. 4. True/False: If f is entire and |f(2)| 2 1 for all z E C, then f is a constant function. 1+ |z| 5. True/False: If f is entire and |f(z)| > 2 for all z E C with |2| > 1, then f is a constant function.