(a) Define property (2:) of a function f : R > IR by 3A 6 R, with A > 0, such that V3: 6 R, A R that satisfies the property (*). There is no need to justify your answer. [1 marks] (ii) Prove that if a function f : R > R satisfies (*) . then f is not surjective. [2 marks] (b) Let Q be a finite set and A, B Q (2. Define f :'P(A) > 19(A) by f(0) = C\\B for 0 g A. (i) Show there exists a finite set (2 and A, B (_2 Q with Am B 7 (0, such that f is not injective. [2 marks] (ii) Prove that A n B = 0 if and only if f is injective. [8 marks] (iii) Determine, with justification, if f is surjective. [2 marks]