4) Suppose that Marsha, Jan, and Cindy each have transitive preferences over oranges, apples, and pears. (Ignore quantities, all we're talking about is who likes what fruit better; so, for example,

Marsha's preferences could be apples oranges, oranges pears, and thus by transitivity, apples pears.) Suppose we define "group preference", ZG, by simple majority vote: for example, "apples ZG oranges" means that at least two of Marsha, Jan, and Cindy have preferences where apples oranges. Show by example (i.e., specify each consumer's preferences over the 3 fruits) that it is possible that G is not transitive even if Marsha, Jan, and Cindy's preferences all satisfy transitivity. (Hint: The solution here is often referred to as the "Condorcet Paradox", or paradox of voting. The Wiki for this is actually pretty informative and is a decent place to nerd out if you're interested.)