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I tried searching for conjunctive usage within negative imperatives but was unable to find any results. I may have just used the wrong search string. My question is as follows.

In the following example, which conjunction is appropriate, 'and' or 'or'? Is it dependent upon context and changes with different usages or is this something consistent with a rule that can be applied more or less systematically?

Don't eat and drink on the bus vs. Don't eat or drink on the bus

Thanks in advance for the help!

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As Robusto's answer suggests, saying "Don't eat or drink on the bus" is equivalent to saying "Neither eat nor drink on the bus"—that is, don't do either thing.

A artificial-intelligence machine reading "Don't eat and drink on the bus," after correctly parsing the "Don't eat or drink on the bus" instruction, might infer that the "eat and drink" prohibition was only against combining the two activities—as a parent might tell a child "Don't run and carry scissors," even though the parent might have no objection to the child's running (without scissors) or carrying scissors (without running).

But human beings' brains are sophisticated enough to recognize that the prohibition against "eating and drinking" on the bus is intended to be inclusive ("don't eat or drink or eat & drink on the bus") rather than exclusive ("don't eat & drink on the bus, but it's okay to eat or drink on the bus"—or for that matter, "don't eat or drink on the bus, but it's okay to eat & drink on the bus," in the case of the "don't eat or drink on the bus" prohibition).

This is not a situation where sentence structure or literal wording or formal logic dictates the correct meaning. Instead, it's a matter of sensibly interpreting the speaker's or writer's intention, based on such relevant details as how bus drivers, bus owners, and other passengers feel about people spilling drinks and/or leaving garbage from their meals on the seats and floor of a bus.

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These are just two different ways of saying the same thing.

Don't eat and drink on the bus

may have some very slight implication of doing both activities at the same time, but I doubt anyone will pause to reflect on that long enough to draw any distinction from

Don't eat or drink on the bus

It's six of one, half a dozen of the other.

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