Because of the transitivity assumption, no two indifference curves for a given consumer can ever cross. Exhibit 4 shows why. If bundle a and bundle b lie on the same indifference curve, the consumer must be indifferent between the two. If a and c lie on the same indifference curve, she must be indifferent between these two bundles as well. But because bundle c contains more of both wine and bread than bundle b, she must prefer c to b, which violates transitivity of preferences. So we see that indifference curves will generally be strictly convex and negatively sloped, and they cannot cross. These are the only restrictions we place on indifference curve maps.