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Usage and Grammar
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).