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' if and only if 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 p100 > p'100, or P100 = p'100 with p50 > p'50, where (p100, P50) and (p'100, p'50) stands for 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.)