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Consider the following sentence:

A project is a large and/or complex undertaking.

To me, the expression “and/or” seems redundant since in formal logic “or” implies “and”:

 Table: truth table for            Table: truth table for            Table: truth table for
 logical OR (i.e. ∨).              logical AND (i.e. ∧).             exclusive OR (i.e. ⊕).

 -----------------------           -----------------------           -----------------------
    A       B     A ∨ B               A       B     A ∧ B               A       B     A ⊕ B
 ------- ------- -------           ------- ------- -------           ------- ------- -------
    F       F       F                 F       F       F                 F       F       F
    F       T       T                 F       T       F                 F       T       T
    T       F       T                 T       F       F                 T       F       T
    T       T       T                 T       T       T                 T       T       F
 -----------------------           -----------------------           -----------------------

Hence, I simply use “or” in place of “and/or”:

A project is a large or complex undertaking.

To me this implies that a project is:

  1. Either large.
  2. Or complex.
  3. Or both.

Am I correct?

On the other hand, using “either/or” seems to imply exclusive “or”:

A project is either a large or a complex undertaking.

This implies that a project is:

  1. Either large.
  2. Or complex.
  3. But not both.

If using “or” does imply “either/or/both”, then I believe that it's incorrect to use “and/or” at all. Am I correct in assuming so?

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    "Or" may include and in formal logic, but in natural language, it means XOR. Do not try out people's patience interpreting natural language as formal logic. When asked if you want cream or sugar with your coffee, or whether the new child is a boy or a girl, do not reply yes. – oerkelens Nov 27 '14 at 7:56
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    @oerkelens So, do you want cream and/or sugar with your coffee? – Diligent Key Presser Nov 27 '14 at 11:10
  • @MadSorcerer: No :) I drink straight. – oerkelens Nov 27 '14 at 12:15
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    Is it a boy xor a girl? – ADTC Nov 27 '14 at 12:37
  • @oerkelens Not exactly. In natural language, it means "exactly one of the choices provided", which only means "xor" when there are two choices provided. In response to "You can have an apple, a banana, or an orange.", "Okay, I'll have all three please." is probably not acceptable, even though true xor true xor true is true. – hvd Nov 27 '14 at 13:52
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The or of English is not equivalent to the or of formal logic. In many cases, English or actually means the exclusive or of logic. For instance, if you say:

Turn left or right at the intersection.

it’s exclusive, because it’s not possible to do both. Or you might ask:

Are you having a boy or a girl?

(Although a logician having fraternal twins might humorously answer “yes”.)

As a result, the phrase and/or is used to make it clear that the inclusive sense is intended.

However, there are many contexts where it’s clear that only the inclusive meaning makes sense. In this case, you can simply say or and be understood. Your example sentence is such a case -- no one would assume that large and complex are mutually exclusive (in fact, one often implies the other). Another example is:

He can’t read or write.

This last sentence also obeys de Morgan’s Law, as it means the same thing as

He can’t read and he can’t write.

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    I could either take your word for it or ask for a citation. – Aadit M Shah Nov 27 '14 at 7:51
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    I've given examples. – Barmar Nov 27 '14 at 7:58
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    He will probably have to cite all of his English teachers who taught him in all the schools he studied. – ADTC Nov 27 '14 at 12:41
  • I was originally going to cite the fact that I've been speaking the language for 50+ years, as well as programming for 35 of them, so I have experience with both uses of OR. – Barmar Nov 27 '14 at 12:48
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    The logician would answer "yes" to "Are you having a boy or a girl?" without needing twins. "I am having a child. If that child is a boy, I am having a boy or a girl. If that child is a girl, I am having a boy or a girl. Therefore, yes, I am having a boy or a girl." – David Richerby Nov 27 '14 at 14:55
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Just to add to the confusion, this would be my answer, and yes, it seems to contradict the accepted answer. So be it. ;-)

Yes, most of the time you should in fact write or instead of and/or.

In cases where you do not want the and/or meaning of inclusive OR, make that clear explicitly: A or B, but not both.

With no additional context or qualification, or is ambiguous in English. Given that, the default understanding by a listener is (as is usual in interpretation) to allow the greatest number of possible interpretations.

In other words, someone hearing or and not knowing which meaning is meant will entertain all possibilities that make sense in the given context.

To narrow things down, you provide additional context, or you make clear (explicitly) that you mean exclusive OR, not inclusive OR.

Examples that involve phrases such as "boy or girl" provide such context (hermaphrodites are typically ignored), so it is unnecessary to add "but not both". (Such examples really do not help to elucidate this question, without additional explanation.)

Why should you write or instead of and/or? Because that's the way we speak. English speakers already listen to or in the way I described above. Using and/or is stilted; it sounds artificial and draws attention unnecessarily to something unimportant. (Or if used to for an important distinction then it is too weak - make the distinction explicit.)

Worse: using and/or can actually confuse readers, in part because once you start using it a reader will expect you to use it consistently, and you won't! Or if you do somehow use it consistently, the result will be almost unreadable (or is too common a word).

Keep it simple: write the way English speakers speak. That lets you take advantage of the way they understand, without making them jump through additional hoops requiring special parsing of your language.

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I'm surprised that no one has cited Strunk and White -- consummate authorities on English usage -- who settled this issue long ago. From Strunk and White, The Elements of Style, Fourth Edition, pg. 40:

And/or. A device, or shortcut, that damages a sentence and often leads to confusion or ambiguity.

In place of:

... would an honor system successfully cut down on the amount of stealing and/or cheating

White says to write instead:

... would an honor system successfully cut down on the amount of stealing or cheating or both.

So there you have it. OR, AND, and XOR all accounted for in the most elegant way possible.

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