Lionel likes extreme sports and follows the five Rules of Actional Thought. He is indifferent between spelunking and a deal with a 5/6 chance of an Arctic canoe trip and a 1 /6 chance of a game of Jai...

Lionel likes extreme sports and follows the five Rules of Actional Thought. He is indifferent between spelunking and a deal with a 5/6 chance of an Arctic canoe trip and a 1 /6 chance of a game of Jai Alai. He is also indifferent between a game of Jai Alai and a deal with a 4/9 chance at spelunking and a 5/9 chance at a bird watching outing. Finally, he is indifferent between cliff diving and a deal with a 2/9 chance of spelunking and a 7/9 chance of a bird watching outing. Given this information, how many of the following three relationships are consistent with Lionel's preferences?

a. 0 c. 2

b. 1 d. 3