You are shown four envelopes. Envelope A contains $1,500; envelopes B, C and D contain uncertain amounts of money but with the following probabilities: Envelope B -- $5,000 with a 10 percent probability, $1,500 with an 89 percent probability, and $50 with a one percent probability. Envelope C -- $1,500 with an 11 percent probability and $50 with an 89 percent probability. Envelope D -- $5,000 with a 10 percent probability and $50 with a 90 percent probability. Show mathematically that if envelope A has a higher expected utility than envelope B, then it must be true that envelope C has a higher expected utility than envelope D. (Note: For a given value of M, U(M) is a fixed but unknown number; DO NOT assume U(M) = M!!)