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, Those properties obey the following principles:
- Each white object is also circular.
- Not all thin objects are black.
- Each rectangular object is also either thin or white or both thin and white.
Consider the following statements:
- If there is a thin object in the set, then there is also a white object.
- If there is a rectangular object in the set, then there are at least two objects.
- Every fat object in the set is circular.
Which of the above statements must be TRUE for the set?
- $(i)$ only
- $(i) \text{ and } (ii)$ only
- $(i) \text{ and } (iii)$ only
- None of the statements must be TRUE
- All of the statements must be TRUE