What is the average reader most likely to guess that “If they don’t have A or both B and C” was exactly intended to mean?

There is a sentence saying "If they don't have A or both B and C,"

I interpret it means "If they have no A or if they have neither B or C". Am I correct?

The condition seems to me that having only B or C alone is not enough, but having A alone is OK and having both B and C is OK too even if A is missing. I am not sure.

Solution 1:

I don't believe you're correct, but your re-statement of the condition is even more obscure.

The verb is only mentioned once, so it must apply to both conditions. There are two conditions, because there is an or and the and is part of "both B and C" — the both links B and C together.

The statement can't actually be reduced any more, but let's say it's

If they don't have A or both B and C, then X.

• If they don't have A, then X
• If they don't have both B and C, then X

The way to prevent X is to have either A or both B and C together. A real-world example is needing identification: you can get a discount with either a photocard driving licence (showing name, address and photo) or both a passport (name and photo) and a utility bill (name and address).

It would certainly be easier to say "X unless they have A or both B and C."

Solution 2:

Above-average reader parses it this way.

I can have thing A. I can have both things B and C. I could actually have all 3 things.

Any of those would meet the condition. Having only thing B without thing C does not meet the condition.

If this was written as a pseudo-code query for a database:

(If A) OR (If B AND C), then proceed...