(b) For a,bN, the relation R defined as (a,b)R if and only if kZ,a=3kb. Prove that R is an equivalent relation, and identify all elements of the set [3]{xRx9}{xRx20.01} (where [3] denotes the equivalence class containing 3). (10 Points) Question 5 (20 Points): Basics on Functions (O1,O2) a) For each of the following maps, identify whether it is a function. If your answer is yes, identify 1) its image and whether it is 2) injective, 3) surjective, 4) bijective; if your answer is no, explain why. i) f:RR,f(x)=x+0.5(x is the biggest integer that is not larger than x, whereas x is the smallest integer that is not smaller than x ). (5 Points) ii) f:RR+,f(x)=ecos(x). (5 Points) iii) Let S be the set of people who are currently UG students of HKU. f:SS,f(x)=xs brother(s). (5 Points) 2 b) Prove that 2x=x+x+0.5 holds for any xR. (5 Points)