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Does "any object in A and B" in English mean

  1. any object in A and any object in B;
  2. any object in A or any object in B; or
  3. any object in the intersection of A and B?
    Thanks a lot.

Another question is that if one wants to express 1, should it be "any object in A or B", or is there another simpler way to express 1? Thanks a lot.

Any helpful answers would be greatly appreciated.

  • It would definitely not mean or (2) and probably does not mean 3. For three one would say "any objects in both A and B." (And please note that the statement itself is in English, so your title is a bit of a puzzlement.) – Robusto Apr 3 '15 at 13:34
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    In general English, it is ambiguous and could mean any of several things. When expressing logical relationships in words, much more detail is needed than this. – Kris Apr 3 '15 at 13:39
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    I would understand it to mean any object that appears in set A as well as in set B. – TRomano Apr 3 '15 at 14:08
  • Thank you all for your comments. I am wondering, what is a simpler way to express 1? Thank you very much. – user2313 Apr 3 '15 at 14:17
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    A simpler way to express (1) is any object in the intersection of A and B. That's precise. English isn't. The English conjunction and is not the same thing as the dyadic functor And. – John Lawler Apr 3 '15 at 15:16
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In mathematical terms, "any object in A and B" expresses x in A and B at the same time. So definitely 3 -- intersection of A and B.

With respect to:

any object in A and any object in B

... think any x in A and any y in B.

any object in A or any object in B

... think any x in A or any y in B.

any object in A or B

... think any x in A or B. (Very much like you expressed it.)

Aside: in that last one, be wary that there is an ambiguity, because the logical OR (as in A or B, one or the other or both) is not a XOR (exclusive OR, as in A or B, but not both). That but not both is a way to resolve this in "layman" speech, but seeing how most people confuse OR and XOR you're usually better off also writing or both to make the logical OR explicit.

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The most well known context in which I think #1 occurs is the stereotypical Chinese menu, where diners could create a fixed-price, family-style meal by choosing items from different categories (appetizers, entrees, etc.). This was typically expressed as Choose 1 from Column A, 2 from Column B, .... Conjunctions like and and or were avoided to prevent ambiguity.

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