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In mathematics, "A or B" includes "A and B".
Does "either" mean "A or B but not (A and B)" or does it include the possibility of "A and B"?
The context might be mathematics, formal logic or ordinary language.

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5 Answers

up vote 15 down vote accepted

"Either A or B" most precisely means, in symbolic logic terms, "A XOR B", where XOR is the "exclusive or". So yes, it means "A or B but not both". It isn't always actually used with full precision, though, so, as usual, context has to be taken into account. If somebody says, "select either A or B", for example, they definitely mean that you should not select both. If they say "if either A or B is true", though, they probably mean a non-exclusive OR, and the condition is still true if both A and B are true. Unfortunately, if there's a generally reliable rule for telling which is meant, I'm failing to think of what it would be.

Without the "either", the presumption would be more toward "A OR B", where OR allows the case where both are true. Which is why computer geeks and propositional calculus nerds will, when asked "do you want to go to lunch now or later?", answer "yes". (Illustrating that the "either" part is implied by context as often as it's cancelled by context.)

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+1 for the lunch part – ghshtalt Feb 23 '11 at 17:20
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If someone puts emphasis on the words "either" and "or" ("You may have either tea or coffee") - either with italics or intonation - that is a fairly reliable clue that the exclusive meaning is intended. – psmears Feb 23 '11 at 19:49
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Man, my family hates when I answer "yes" to or questions. :-) – T.E.D. Jul 11 '11 at 15:05
up vote 5 down vote

Either A or B means the same as A or B. Each can mean or used in the inclusive or exclusive sense.

Usually, the inclusive sense is used in mathematics and the exclusive sense in everyday life. In any case, further specification or context will remove any doubt.

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up vote 1 down vote

From wikipedia:

Either/or means "one or the other." Its usage, versus the simple or structure, is often for emphatic purposes, sometimes intending to emphasize that only one option is possible, or to emphasize that there are only two options. Its use in a sentence lets the reader/listener know in advance that a list of two or more possibilities will be given.

As you correctly recognize "or" used alone can also include the possibility of both A and B (especially important in mathematics).

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up vote 0 down vote

It means that it can't be both. I believe one would call it an "exclusive or" or XOR.

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What a great idea! You saved me lots of money! I have to pay income tax if I either live or work in this state... but now I know that (since I both live and work here) I do not need to pay taxes. Wow! – GEdgar Jul 11 '11 at 14:05
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While the standard explanatory text may say "either live or work," I am sure your state's tax code is a little more specific in its wording so as to avoid such an intentional misreading by an antagonistic reader. – horatio Jul 12 '11 at 13:58
up vote -1 down vote

I think you have confused yourself in some sense. "A or B" includes A or B or both. That needs to be clear.
Usage of 'either' as a conjunction has different meaning than 'Or' as it means 'A' or 'B' but not both.

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No. In everyday language, "A or B" usually does not include both, though it may sometimes. "Do you want tea or coffee?" implies not both - if you answer "both" you are stepping outside the norm. – Colin Fine Feb 23 '11 at 18:03

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