1. [4 pt] Let f : A - B be a function. For any set C C A and D C B, we define . the image of C, denoted by f(C), to be the set f(C) = {y E B| there exists some r ( C s.t. y = f()}( ie., f (C) = {f(x) ( B|x E C}). . the pre-image of D, denoted by f-'(D), to be the set f(D) = [re Af(x) ED) For each of the following statement, determine if they are true or false, by either proving it or giving a counter-example. a) For any Cl, C2 C A, f(CinC2) = f(CI)nf(C2). b) For any CI, C2 C A, f(C1 \\ C2) = f(CI)\\f(C2). c) For any DI, D2 C B, f-'(D UD,) = f(Dj)Uf (D.). d) For any Di C B, f-'(DA) = (f-'(D1) ). Remark Your solution should be of the following format: . Either "The statement is true, as is justified by the following proof. Proof:...." . Or "The statement is false, as is disproved by the following counter- example. Counter-example:...."