PROBLEM (1) (Rational Choice) Suppose your friend is about to buy a digital camera. A digital camera is identified with three dimensions; 1) resolution (in megapixels), 2) optical zoom (a real number) and 3) battery life (a number of hours). For example, A = (8, 4, 20) is a camera with 8mp resolution and x4 optical zoom and 20 hours of battery life. When he goes into a store, he faces a menu of cameras. When comparing two cameras if camera A is weakly better than B on at least 2 dimensions, it is weakly preferred to the other; written A 2preferred B. a) Is this preference relation complete? Transitive? Prove it or show an example where the property doesn't hold. b) Suppose the agent chooses from any menu of cameras, a camera that is (weakly) preferred to all other cameras in the menu. Would this choice function be rational, given (a)? Briefly explain your reasoning