"or" in English is actually logical xor, which means that when we actually need to express logical or, we have to implement it in terms of other operators; hence "and/or", i.e. "and xor xor"
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Start with not: "no, not that" becomes "neither that nor itself" Which can be used to implement or: "coughing and/or sneezing" becomes "not neither coughing nor sneezing" And is slightly more complex: "dinner and a movie" becomes "neither (not dinner) nor (not a movie)"
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Finally, xor, which we can build from and: "soup or salad" becomes "neither (soup and salad) nor (neither soup nor salad)" which is actually pretty readable!
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of course, using "and" is kind of cheating; if we really want to use just "neither", then we have to write: "neither (neither (neither soup nor soup) nor (neither salad nor salad)) nor (neither soup nor salad)"
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