Problem 4. (max. 30 = 10 + 10 + 10 points) TRUE OR FALSE??? For each of the following statements, determine whether it is correct or not, and then fully justify your answer. (a) If F = (f, g, h) is a divergence-free smooth vector field on R3 (where we denote the coordinates in the standard way, by x, y and z), then div(x F) = V.(xcF) = f (recall that we write x for the Ist coordinate function, that is, x(x, y, z) = x for all (2, y, z) ER3 ). (b) If w and n are closed one-forms on R3, then w An is also closed. (c) There exists a vector field G on R3 such that curl G = V xG = (x + y, y - 2z, 2x - 3z)