2) Let us try to clarify the content of the independence and continuity axioms and the difference between them. a) Consider H, whose preferences over lotteries with only two prizes ($100, $0) are as follows: H strictly prefers lottery L to lottery L' iff p > p' where p and p' (respectively denote) the probability of $100 prize in lotteries L and L'. Does H's preferences over lotteries on ($100, $0) satisfy continuity, independence? (Do not just answer Yes, or No. If you say Yes, clearly show why. If you say No, then provide a counterexample.) b) Now, consider E, whose preferences over lotteries on prizes ($100, $50, $0) are as follows: E strictly prefers lottery L to lottery L' iff either Pix. > P 120 . Or Pino = P'ing With Pso > P's where Pino . Pso Piano and p's (respectively denote) the probability of $100 and $50 prizes in lotteries L and L'. Does E's preferences over lotteries on ($100, $0) satisfy continuity, independence? (Do not just answer Yes, or No. If you say Yes, clearly show why. If you say No, then provide a counterexample.)