False.
A rational consumer would choose between points A and B based on their preferences and budget constraint. If point A provides a higher level of satisfaction and is affordable within the budget, the rational consumer would choose point A. However, if point B is more affordable and still provides a satisfactory level of satisfaction, the consumer may choose point B instead.
Similarly, if the consumer is indifferent between points B and C, they would choose the point that is most affordable and provides a satisfactory level of satisfaction. It is not necessarily true that they would choose neither one.
Therefore, the statement "The rational consumer would be indifferent between B and C but would choose neither one" is false.