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Depending on the tone of the spoken question, this can mean:

"Would you like a cup of something to drink?"

If the answer is yes, then further questioning is required to ascertain which drink is desired.

Alternatively, the question as spoken could presuppose a "yes" answer and could be asking which which drink is desired.

1. In written English, to avoid ambiguity, what is the most succinct way to express the exclusive "or", ie "one or the other, but not both"?

2. In written English, to avoid ambiguity, what is the most succinct way to express the inclusive "or", ie "one or the other, or both"?

Any ideas?

Doug
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1. Would you prefer a cup of coffee or tea?
2. Nothing is striking me that is particularly succinct.
The17pointscale1. Would you prefer a cup of coffee or tea?
To which I would reply, 'Yes, I would prefer one or the other.'

The meaning is conveyed by the tone of spoken question.

I think we should allow 'xor' as part of standard English.

What do you think?
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So then

'xor' would mean the 'exclusive or'.

'or' would mean the 'inclusive or'.

How 'bout it?
Tricky stuff.

Either...or is normally seen as exclusive disjunction.

EG

Either I will go swimming or see a movie. (I can also choose to do neither.)

But, in some contexts, either...or can be read as inclusive disjunction:

Father to teen son: Either see a movie or go swimming. Don't sit round here whining all day! (You must do at least one of those things,
but you are not precluded from doing both.)

........

So, transfering that to your example:

"Would you like (either) a cup of tea or coffee?" can only be exclusive, IMO., whereas "Have a cup of tea or coffee." could be either exclusive or inclusive - depending on whether it is an offer/suggestion or and "order".
In my opinion, when considering disjunctions, context is much more important to determining whether an "or" is inclusive or exclusive than the presence or absence of an "either."
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DouglasM6So then

'xor' would mean the 'exclusive or'.

'or' would mean the 'inclusive or'.

How 'bout it?

An exclusive OR is often called an XOR or EOR.
Would you like a cup of tea or coffee? - offering

Did you want tea or coffee? has to be said carefully to avoid sounding rude but makes the assumption that a drink is wanted.

Was it tea or coffee you wanted? as above

Tea or coffee? Very clear that a drink is wanted and just offering the choice of which.
Waiter: «Tea or сoffee?»
Petya: «Coffee.»
Waiter: «Ha! You didn't guess it. Tea!»
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