One or more of A, B, C, [and, or, and/or] D?

In the expression "one or more of A, B, C, [and, or, and/or] D," what is the correct conjunction? Examples of all three choices abound with apparently equivalent intended meaning.

• "One or more of {A, B, C, D}." The set one is mentioning a non-empty subset of comprises A, B, C and D. – Edwin Ashworth Aug 29 '13 at 14:27
• @EdwinAshworth really? You wouldn't use or? As in one or more of dogs cats *or* fish are allowed? Would you say one or more of dogs cats fish are allowed? – terdon Aug 29 '13 at 14:45
• Following Zibbobz' mathematical logic, then, in examples where more than one of one of the choices is not particularly meaningful, then the correct conjunction must be "and." For example, in "an alloy comprising one or more of iron, zinc, and tin," the quantity of each element is inherently arbitrary, and it would not make sense to have 2 irons, for example. – user50779 Aug 29 '13 at 15:02
• @user50779 I think "one or more" would be incorrect to use in describing an alloy, because you need all of the compoents to make it. The "or" in "one or more" implies you can create the alloy without adding any further elements, which is incorrect. And I can't think of any other way to make this seem correct, because I can't think of any cases where such a distinction would be possible. – Zibbobz Aug 29 '13 at 15:16
• I disagree! An alloy needs a minimum of two elements. You do not need all of the components. In this example, the "comprising" language is open-ended in that additional elements can be present. So an alloy comprising one or more of iron, zinc, and tin could be an alloy consisting of iron and zinc (only); iron, zinc, and tin; iron and chromium (since only one of the listed elements must be present); etc. – user50779 Aug 29 '13 at 15:42

They do actually have different meanings, but it's very subtle..

"One or more of A, B, C and D" means that of the sets a, b, c and d, you have one of (or more) the options available, with the set A, B, C and D inclusive. Possible sets include any combination of A, B, C, D, but not multiples of any of the set (So, for example, you could pick B, C, D as your set, but not B, B, C).

"One or more of A, B, C or D" means you have the option to pick "one or more of" the defined choices, but not more than one of the set. So you could pick as many of A, B, C, or D that you desire, but you may not mix (A set of A, A, A is acceptable, but a set of A, A, B is not).

The reason for this is that "or" is an exclusive operator. It allows for any choice to be made, but only ONE choice. "And", on the other hand, is inclusive, and allows any choice to be made within the set. So "one or more" of the set "A, B, C and D" allows for any choice to be made on which letter is included, but does NOT allow for multiples of the set.

The last case, "One or more of the set 'A, B, C and/or D'" actually has a hidden operative. The "/" symbol conjoins the two operators, so it allows for BOTH operators to apply. In other words, it removes the limtation of either operator and allows for multiples of each choice AND more than one choice.

• +1 I think you are right, but your analysis may not occur to everyone. See discussion below. – bib Aug 29 '13 at 16:17
• If we're going to use mathematical logic as the standard, then a list connected with "or" – user50779 Aug 29 '13 at 16:25
• If we're going to use mathematical logic, then a list connected with "or" is "true" (1) for all input values except for everything "false" (0). Thus, "A, B, C, or D" includes the set {A, B, C, D, AB, AC, AD, BC, BD, CD, ABC, ABD, ACD, BCD, ABCD}, and "one or more of" allows repeats of any of these combinations. But strict mathematical logic does not necessarily apply to common language usage in English. For example, following the above interpretation of "or," the usage "and/or" is redundant with "or" and should never be used! So I would be careful about applying strict rules of logic. – user50779 Aug 29 '13 at 17:26
• I believe that the 'of' renders the reading given in the third paragraph ungrammatical. *'Pick two or more of apples, bananas, citrons or damsons.' It would have to be 'Pick two or more apples, bananas, citrons or damsons.' (I've changed to 'two or more' to avoid agreement conflicts.) The first reading corresponds to 'Pick one or more of the following: item A, item B, item C (,/&) item D'. – Edwin Ashworth Aug 29 '13 at 23:58

I think Zibbobz is correct in his analysis, but I fear most readers would not immediately (or perhaps ever) recognize the subtle distinctions. How can we make clear which of the three choices we mean?

(1.) Multiples permitted across categories, but not within categories (A or AB or CDE, but not AA, or ACC)

One each from one or more categories of A, B, C and D

(2.) Multiples permitted within one category but not across categories (A or AA or BBB, but not AB or ABB)

One or more from one category of A, B, C or D

(3.) Multiples permitted from one or more than one category (A or AA or AAB or AABB)

One or more from each of one or more categories A, B, C and D

Obviously none of these are as succinct as the versions offered, but these are less prone to misinterpretation.

• Your first example doesn't seem to make sense to me, because "one from" suggests exactly one item, yet "one or more" suggests multiple, where only one item is being requested. I think for your first example, you would want to say "One each from one or more of categories A, B, C and D". – Zibbobz Aug 29 '13 at 17:05
• @Zibbobz I think the logic holds, but I think your suggestion is better and will modify accordingly. – bib Aug 29 '13 at 17:35