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I was recently given a math question which was stated: "...divisible by 2 OR 3". I believed at that point that this did not include numbers such as 6 as the word OR implies that it is the choice between 2 statements, therefore leading to the conclusion that there when "or" is stated, it does not mean AND. It is true that OR does indeed mean AND as well as just the choice between two statements? I am simply asking for a explanation for what the word OR means; does it include the word AND. Thank you. FULL QUESTION IS, IF YOU WANT IT: How many numbers in a sequence from 0 to 2000 are divisible by 2 OR 3?

Avyay Varadarajan
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    Don't know if it actually is, but i smell a duplicate. – Sakatox Mar 11 '16 at 23:06
  • I did have a look for duplicates but I haven't seen anything exactly equivalent yet. – John Clifford Mar 11 '16 at 23:07
  • In that particular context it is true that or means and. However if I say please go to the shop and buy some meat or some fish in that case or does not mean and. It means either one or the other. – WS2 Mar 11 '16 at 23:08
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    @WS2 That reminds me of one of my favourite programmer jokes: a programmer's wife says to him "Go to the shop and get a pint of milk, and if they have eggs buy six." So he goes to the shop and comes back with six pints of milk. When his wife asks why he has so much he replies "They had eggs." – John Clifford Mar 11 '16 at 23:15
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    We can never be too careful with differentiating between common and logical OR! Just be on the safeside and ask back if the initial question was unclear/ambiguous. @JohnClifford oh god, I tried to avoid mentioning that one :D – Sakatox Mar 11 '16 at 23:20
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    @Sakatox I'm a .NET Developer, programmer jokes are my specialty. ASCII a stupid question, get a stupid ANSI. ;) – John Clifford Mar 11 '16 at 23:22
  • @JEL This is a completely different question. I am asking if the word OR includes AND as well, unlike the other qustion. – Avyay Varadarajan Mar 12 '16 at 00:20
  • Logic exists in many spheres. – user116032 Mar 12 '16 at 00:27
  • @AvyayVaradarajan, I understand yours is a different question. However, your question asks about the inclusive and exclusive senses of 'or' in English (not artificial languages), as does the (possibly) 'duplicate' question, and the accepted answer of the 'duplicate' directly answers your question. The rest of the discussion and the other answers at the 'duplicate' question should prove useful not only to you but to others with similar questions about 'or'. Your question is good. ['Duplicate', oddly for a site devoted to the use of English, is misused here at EL&U to mean 'closely similar'.] – JEL Mar 12 '16 at 08:09

3 Answers3

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Semantics of OR are "contextual". Linguistics usually don't bother with the distinction, or rather, don't mix the concept of the two.

Generally speaking, only those contexts that deal with logic require the distinction, and in turn, everyday speech lacks it.

Look up the truth tables for OR and AND. They are not equivalent, Logical OR is true when either part of the expression evaluates to/is true.

Yes, in this context, it includes the AND case.

Also, sidenote: The title might be misleading, please correct/edit to reflect context.

Sakatox
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Taken in this context, 6 would be included; the OR simply means "divisible by at least one of these" which would still count if it's divisible by both.

There is a logical construct called XOR, in programming and circuitry at least, which will return true when only one of the two possibilities is true, but that's not the case here.

John Clifford
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    I think the context, a math question, makes it eligible for XOR. – Sakatox Mar 11 '16 at 23:09
  • I don't often see XOR used in purely mathematical contexts, but it's possible that a problem would specify it, sure. – John Clifford Mar 11 '16 at 23:10
  • Math divisibility is an open conditioned issue, I think numbers that are divisible by 6 should be divisible by 2 and 3. This, and the nature of the question indicates XOR and AND, aka classic OR. – Sakatox Mar 11 '16 at 23:18
  • @Sakatox But if it were divisible by 2 XOR 3, 6 would return false as it's divisible by both. 4 or 9 would be fine, though. – John Clifford Mar 11 '16 at 23:19
  • There's only so much leeway to be succinct with maths without rambling or losing meaning. Our teachers always encouraged us to ask back or assume what's most common - that being covering all cases (OR, AND, XOR in this). – Sakatox Mar 11 '16 at 23:24
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I've to disagree we can't answer so far we still miss the complete question of the problem.

In math (statistical computing) :

  • "OR" is +

  • "AND" is x

OR formally excludes AND ; it's always an altenative even in general speaking.

In fact, I guess you were expected to answer if you could divide by 2 or 3 something. But you fell in the trap ! It was divisable by both & you were supposed to see it... You should have say it because it wasn't divisable either by 2 or 3.

It is not a question of vocabulary but straight logic !

DAVE
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  • Let's say I have two binary inputs, A and B. In A OR B, I get true if A is 1, B is 1, or A and B are both 1. In A AND B, I only get true if A and B are both 1. OR not only doesn't formally exclude AND, it includes matches that AND doesn't. – John Clifford Mar 11 '16 at 23:34
  • Following on from this, if I'm asked for a number that divides by 2 OR 3, I could have 1, 2, 3, 4, 6, 8, 9, 10.... but if asked for one that divides by 2 AND 3, I'm limited to a subset of those possibilities: 6, 12 etc. – John Clifford Mar 11 '16 at 23:35
  • @DAVE Actually the question was asking to find how many numbers in a sequence from 0 to 2000 were divisible by 2 OR 3. – Avyay Varadarajan Mar 11 '16 at 23:56
  • OK folks ! So far iyour list, AVYAY, has numbers divisible by "both" 2 & 3 (ie. 6 ; 12 ; 18 ; 24 ; 30 ; 36 ; 42 etc...) if you only get the divisible by 2 your answer is wrong. – DAVE Mar 12 '16 at 09:20
  • From 0 to 20, you'd have : Div by 2 : 2 4 (6) 8 10 (12) 14 16 (18) 20 & Div by 3 : 3 (6) 9 (12) 15 (18) – DAVE Mar 12 '16 at 11:26