The word "and" is the appropriate choice here, if the intended meaning is that all three things are prohibited.
I've read a justification for using "or" in situations like this, and there's a subtle logical error in it. This is not going to be relevant in GMAT SC, but I'll point it out anyway - for interest only!
The justification for using "or" goes like this:
- if we say "X, Y, or Z", we mean one or more of these things
- so if we say "*not* X, Y, or Z" we mean "not one or more of these things", so we mean "none of these things"
- when we list things after a verb like 'prohibit', 'ban', 'forbid', or 'proscribe', a verb where the meaning "not" is implied, we usually mean "none of these things" are allowed, so we should say "or", not "and"
That is logically correct if your sentence reads as follows:
1. "You are allowed to eat things that are not meat, tomatoes, or lemons"
That means meat, tomatoes and lemons are all forbidden. We need to use "or" here to convey that meaning. This sentence has a different meaning:
2. "You are allowed to eat things that are not meat, tomatoes, and lemons"
This only means you'd be allowed to deviate from a diet consisting of meat, tomatoes and lemons.
But that consideration isn't relevant when you consider a sentence like this:
3. "You are not allowed to eat meat, tomatoes and lemons."
This does not mean the same thing as sentence #1 above. We can't just move the word "not" around without changing the meaning of the sentence. When we write a sentence like #3, the word "not" is stuck to the verb. In sentence #3, the verb "not allowed" applies to all three foods in the list. It would mean something different if you used "or":
4. "You are not allowed to eat meat, tomatoes or lemons."
This means something more like "you're not allowed to eat (at least) one of these things, but I'm not telling you which". That's not normally the meaning we'd intend by a sentence like this.
So if we're listing things that are all "prohibited", we need to use "and" in that list.
And just to confirm this accords with general usage, I did do a quick google search to find credible writing which used "prohibited" or "forbidden" followed by a list, and in each example the word "and" was used when the intended meaning was "all of these things are prohibited". So independent of logic, "and" also appears to be the idiomatically correct choice.
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