Q. Is there a general rule on how to interpret a sentence like “The box must be A and B or C”? Does it mean the box must be A, and also either B or C? Or does it mean the box must be either both A and B, or just C?

A. This is the kind of instruction that makes test takers abandon hope. The general order of operations in logic is that *and* takes precedence over *or*: “The box must be A and B or C” means “The box must be (A and B) or (C).” However, a reader is left to guess whether the person who wrote the instruction knew that. Sometimes context gives a clue:

The box must be assembled and blue or black = (A) and (B or C).

The box must be taped and labeled or empty = (A and B) or (C).

The strategic insertion of *either* is a classic aid to comprehension:

The box must be assembled and either blue or black = (A) and (B or C).

The box must be either taped and labeled or empty = (A and B) or (C).