We are given a (possibly empty) set of objects. Each object in the set is colored either black or white; is shaped either circular or rectangular, and has a profile that is either fat or thin. These properties obey the following principles:
1. Each white object is also circular.
2. Not all thin objects are black.
3. Each rectangular object is also either thin or white or both thin and white.
Consider the following statements:
(i) If there is a thin object in the set, then there is also a white object.
(ii) If there is a rectangular object in the set, then there are at least two objects.
(iii) Every fat object in the set is circular.
Which of the above statements must be TRUE for the set?