1. QUESTION 1 Assume A C X. Define dA, the boundary of A as follows DA = An (X - A) Prove the following. (30 points) a) Int(A) noA = 0 b) A = Int(A) UOA c) 8A = 0, if and only if A is both open and closed. d) A is open, if and only if dA = A - A e) Suppose A is open. Is it true that A = Int(A)? If yes, prove it, if no, provide one example to show it is not true. f) Find the boundary of the following sets (you do not need to justify your answer). . In R with the standard topology, A = [0, 1). . In R with the standard topology, B = Q. . In R2 with the standard topology, C= {xxyz>0,y>0}U{xxy|x