“Any object in A and B”—What does it mean?

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.

• 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
• 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
• 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
• 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

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.

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.