# What's the meaning of or/not in logical reasoning questions?

I have a simple problem basically I am unable to understand the meaning of some questions involving or/not, and using comma with and. I have the following questions:

1. What is the meaning of, say:

X does not play football or cricket.

What we can infer from this? Can we say X does not play both of them? Or one of them?

2. How the previous line is different from:

X does not play either football or cricket.

3. If x does not play both of them, why in books such kind of statements are there instead of neither/nor.

4. What is the meaning of:

M and N, who reads newspaper, are not sitting together.

Here, Do M and N, both reads newspaper?

Please clarify these things to me. I am not a native English speaker so I found it very difficult to understand and as in logical reasoning questions these statements are common to see I face lot of problems.

Please also tell me about such more things that can be confusing, may be, provide a link.

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• I think this question would be more appropriate to English Language & Usage or English Language Learners, since it deals specifically with negation in English. – StoneyB Aug 7 '15 at 17:20
• Forget about the comma; that's just punctuation, representing intonation. The meaning problem is called "De Morgan's Laws" in logic. These say that when negated, and and or swap meaning. That is, `(Not P) And (Not Q)` is equivalent to `Not (P Or Q)`; also `(Not P) Or (Not Q)` is equivalent to `Not (P And Q)`. So I didn't see Bill or Max means I didn't see Bill and I also didn't see Max. LIkewise, I didn't see Bill and Max means either I didn't see Bill or I didn't see Max (or maybe I didn't see either one). – John Lawler Aug 7 '15 at 18:22
• I'm voting to close this question as off-topic because it is about logic, not linguistics. – robert Aug 7 '15 at 19:06

Using "or" in a negative statement can be ambiguous.

In your example, the most reasonable interpretation seems to be that "X does not play football" and "X does not play cricket" are both true. But in similar sentences there may be different reasoning. Consider the following (made-up) examples:

If you don't play football or cricket, you can't graduate with honors.

Does it read as if you need to play both?

If you don't pass math or French you'll have to stay and study during the vacation.

This one reads as if you do have to pass both... Although the structure is the same as in the previous example!

Also consider what happens if you change "or" to "and". If the meaning seems to be the same, there is ambiguity in at least one of the sentences.

There are ways to eliminate the ambiguity, and you should try to use them at least in writing, if not in speech:

• When the negation appears as a separate word (like "not", "don't", or "never"), Use "either/or" or "one of" if you mean "not (a or b)"; use "both" (with "and") or "any" to mean "not (a and b)", which is equivalent to "(not a) or (not b)".
• Place the negation with the simple conditions ("either not A or not B").
• For embedded negation, you can use "neither/nor", which means "not (a or b)".

With the first example:

If you don't play either football or cricket, you can't graduate with honors.

(If you do play either one, you can)

If you don't play both football and cricket, you can't graduate with honors.

(You have to play both)

If you play neither football nor cricket, you can't graduate with honors.

(Playing only one makes the condition false, so you can)

If you either don't play football or don't play cricket, you can't graduate with honors.

(Unambiguous)

• RE: "If you don't play football or cricket, you can't graduate with honors." Does it read as if you need to play both? Not at all. If you need to play both, I would expect the conjunction to be and, not or. – J.R. Aug 2 '16 at 21:29
• Your logic is good, but for non-native speakers this can be very confusing. That's the reason I added "consider what happens if you change or to and". – laugh Aug 2 '16 at 21:35

The meaning of "X does not play football or cricket" is unclear. There is a problem of scope, here, as between "not" and "or". If "or" is in the scope of "not", it means "X plays neither football nor cricket", or, that is, "X does not play football and X does not play cricket." That is probably the most popular interpretation.

However, depending on dialect and intonation, there may also be a reading in which the scope relationship is reversed, and "not" is in the scope of "or". You get this if "football or cricket" is focused: "it is football or cricket that X does not play". Then, it means: "Either X does not play football, or X does not play cricket.

You also get that interpretation if material including "not" has been elided: "X does not play football or (X does not play) cricket."

The "not" might also be read as denying the appropriateness of a quoted sentence "X plays football or cricket" that someone has said. For instance, there could be a terminological quarrel -- it's "soccer" that X was said not to play, or cricket, not "football".

You should know that a sentence like "John does not play football or cricket" means, unambiguously, that John plays neither football or cricket; or "It is not the case that John plays football, and it is not the case that John plays cricket". There is a realm of potential ambiguity out there, since some people interpret "or" as meaning "exclusively one or the other", for example "You may have ice cream or cake", which we might interpret as "You may have ice cream, or you may have cake, but not both". The inclusive / exclusive interpretation is really determined pragmatically by context, so when ordering in a restaurant, if the waiter offers "steak or fish", you can't have both -- but when flying first class, if they offer "red wine or white", you can get away with asking for both. Essentially, "but not both" is a pragmatic add-on, not part of the core meaning of "or".