Talk:Exclusive or

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Please remove this part: "Even so, there is good reason to suppose that this sort of sentence is not disjunctive at all. If all we know about some disjunction is that it is true overall, we cannot be sure which of its disjuncts is true. For example, if a woman has been told that her friend is either at the snack bar or on the tennis court, she cannot validly infer that he is on the tennis court. But if her waiter tells her that she may have coffee or she may have tea, she can validly infer that she may have tea. Nothing classically thought of as a disjunction has this property. This is so even given that she might reasonably take her waiter as having denied her the possibility of having both coffee and tea."

The differences between the two examples have nothing to do with or. It's the fact that the conditional "may" is used. If a woman has been told that her friend may either be at the snack bar or may be on the tennis court, she can infer that he may be on the tennis court. Myfirstnameisdanger (talk) 19:46, 7 August 2019 (UTC)[reply]

 Done Implicit consensus since no one has objected and the citation needed tag. --Trialpears (talk) 23:25, 13 August 2019 (UTC)[reply]

In case anyone's still reading, this was an example of a free choice inference for which "or" is very much one of the culprits. I think it would be WP:UNDUE to include free choice in the article at the present moment (given all the other important things that aren't mentioned) but it would belong in a future more developed version. Botterweg14 (talk) 22:01, 11 February 2021 (UTC)[reply]

The system of symbolic logic notation used on this page, with right angle thingies for negation, Vees for "OR", and carats for "AND" is not the only one. What is it called? Is it the most common notation? If not, what is the most common notation? If I wanted to write out a statement of logic on a sign or a T-shirt and have it be recognized by as many geeks as possible, which system of notation should I use? Pciszek (talk) 14:44, 6 June 2020 (UTC)[reply]

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Under the section 'Exclusive "or" in natural language', the former should be changed to the latter:

The English example below would normally be understood in conversation as implying that Mary is not both patriotic and quixotic.

The English example below would normally be understood in conversation as implying that Mary is not both a singer and a poet.

User:Botterweg14's initial draft of this addition used "patriotic and quixotic" as the example, but when this was later changed to "singer and poet", the line above wasn't modified to match. Baitrak (talk) 16:03, 6 April 2021 (UTC)[reply]

 Done RudolfRed (talk) 17:24, 6 April 2021 (UTC)[reply]

@Baitrak: Just so you're aware, your account is now autoconfirmed, meaning that you can edit confirmed protected pages without needing to create an edit request anymore. Sincerely, Deauthorized. (talk) 17:30, 6 April 2021 (UTC)[reply]

Mary example is error. "Mary is a singer or a poet or a dancer" is not 3-XOR. --Voproshatel (talk) 12:49, 18 October 2022 (UTC)[reply]

At least in the introduction, it would be helpful (even to eggheads) to emphasize the basics. xor (exclusive disjunction) means not-equal, reminding the reader that the simplest base notion is actually equality (logical biconditional). Given that, "neq" or somesuch would be a better name, and ≠ or similar would be a better symbol, but neither is likely to change. Dang, those formal names are too long to type twice in one day.

Thunkapedia (talk) 17:19, 8 March 2022 (UTC)[reply]

The sentence "Mary is either a singer or a poet or both." in section Exclusive or in natural language indicates that „either – or” usually indicates an alternative. This is also what one finds in dictionaries; see e.g. [1]. In the Oxford English Dictionary, "either – or" is mentioned in the entry of "either" under "II. Expressing alternatives. 3. In correlative constructions with a conjunction, introducing the mention of alternatives." From this and the article here, my understanding is that in everyday-speech in the absence of negation, it indeed always indicates an alternative.

For me, so far this indicated that in English texts on mathematics and logic “either – or” should be read as exclusive or. I noticed that sometimes “either – or” is used when inclusive or is meant, but I always thought that in such a case the author was just careless and “either” should be deleted.

After I did indeed delete an occurrence of “either” in an article on a mathematical topic for the stated reason, another user and I had a discussion on the use of “either – or” (see User_talk:TakuyaMurata#On "either ... or"). With the discussion, I have now learned that it is not the case that “either – or” means exclusive or, or at least that this interpretation of “either – or” is not generally accepted.

My counterpart in the discussion referred me to this document in which it is unambiguously stated that "either - or" should mean inclusive or in mathematical writing: [2] I also found this article in the field of logic: [3]. Here "principle 3" indicates the same, that is, “either – or” should simply mean 'or', that is, inclusive or.

But I have not found an authoritative source on the question whether “either – or” in mathematics and logic should be interpreted as inclusive or exclusive 'or' or that it might have both meanings.

Of course, “either” by itself can have a meaning in the direction of “any”. This is, for example, the case in “in either case” or “either way” and also in “Suppose either (one) of the following conditions is satisfied”. This does by itself, however, not mean that “either – or” does not have the specific meaning of exclusive or in mathematics and logic. As stated, this is what I thought.

I also mention that my mother tongue is German, and in German we have the expression “entweder – oder”, which means exclusive or and nothing else. So, as “soit – soit” in French, this is a persistent XOR-construction.

To clarify this question and as a reference for further discussions in this topic here in Wikipedia, I would like to suggest that there should be a section in the present article on the use of “either – or” in texts on mathematics and logic. However, for this first a good source should be found. This might be complemented with statements on expressions in other languages like “soit – soit” in French and “entweder – oder” in German. Claus aus Leipzig (talk) 17:11, 19 March 2023 (UTC)[reply]

What is the identity element of this group? 181.209.152.189 (talk) 00:33, 17 April 2024 (UTC)[reply]

T XOR F = T

F XOR F = F

Thus F is the identity element.

Alazn02 (talk) 17:46, 15 May 2024 (UTC)[reply]