Q: How do you interpret a negative construction with “or” rather than “and”? For example, “A pie without strawberries or cherries is awful”? Does it mean a pie needs both strawberries and cherries to not be awful? Or that just one or the other is necessary?
A: Most negative constructions with “or” and “and” are pretty straightforward. Here’s the difference:
“A pie without strawberries or cherries is awful” means both “A pie without strawberries is awful” and “A pie without cherries is awful.” In other words, a pie without one or the other is awful. The use of “or” indicates that the two coordinates, the strawberries and the cherries, are to be considered separately.
“A pie without strawberries and cherries is awful” means that a pie without both of them is awful. The use of “and” indicates that the two coordinates are to be considered together as a unit.
You may be thinking of the complications that arise when the word “both” appears in certain kinds of negative constructions. Here’s how Pat treats this problem in the 4th edition of her grammar and usage book Woe Is I:
BOTH . . . NOT/ NOT BOTH. Using both and not in the same sentence is asking for trouble. That’s because saying something negative about both can be ambiguous. When you say, Both children did not get the flu, do you mean both escaped it? Or that just one—not both—got it? Put the negative part where it belongs: One of the children, not both, got the flu. Or drop both and use neither instead: Neither child got the flu.
In fact, any negative statement with both should be looked on with suspicion. A sentence like There are no symptoms in both children probably won’t be misunderstood. But it would be clearer and more graceful to drop both and use either: There are no symptoms in either child.