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  • A: Positive and negative numbers cannot satisfy the condition.
  • B: Positive or negative numbers cannot satisfy the condition.
  • C: Non-zero numbers cannot satisfy the condition.
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4  
I believe B is grammatically incorrect, and should technically read "Neither positive nor negative numbers can satisfy the equation". –  Urbycoz May 25 '11 at 10:02

4 Answers 4

up vote 1 down vote accepted

If we start with

C: Non-zero numbers cannot satisfy the condition.

what you are asking is, I assume, if the following

A: Positive and negative numbers cannot satisfy the condition.

B: Positive or negative numbers cannot satisfy the condition.

express the same proposition as C.

If I would to transform C I would say

D: Neither positive nor negative numbers can satisfy the condition.

because A is ambiguous and B does not sound right.

In A there is a danger that 'positive and negative' is read as 'numbers that are positive and negative (at the same time)...' which is not intended.

Example

Big and yellow windows should not be opened.

In the case of 'or' it is better logically, but with the negation you would expect 'Neither... nor'.

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How about "Positive numbers and negative numbers cannot satisfy the condition"? –  xport Jun 10 '11 at 14:56

suppose the condition is

x = 0

then A, B, C each are correct

suppose the condition is

x + y = 0

then A is false because if you have (1, -1) then you have positive and negative numbers and you can satisfy the condition.
B is true because in either scenario of having two positives or having two negatives, you have positive or negative numbers and cannot satisfy the condition. C is false for the same reason as A is false.

suppose the condition is

x - y = 0

then A is true because in having one positive and one negative number, you have positive and negative numbers and you cannot satisfy the condition.
B is false because if you have 1,1 or -1,-1 then you have positive or negative numbers and you can satisfy the condition. C is true for the same reason as A is true.

so, if by difference in meaning you mean being able to substitute one for the other without consequence, then an answer to your question will depend on the condition that you have in mind.

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Grammatically and linguistically there's no difference at all, but logically, there is a huge difference.

Since this is an English language forum, I believe you are asking about English; therefore, the answer is: no, there's no difference.

If this were a PHP language forum, for example, I could give you a huge explanation of the difference.

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A and C are equivalent.

B is ambiguous. Beacause there are two kinds of *OR*s

  • Exclusive or - This is Either ... or.... It means, "Either positive numbers or negative numbers cannot satisfy the condition." In this case B is not equivalent to A.

  • Inclusive or - B is equivalent to A.

In writing, it is ambiguous but while speaking speaker (good speaker) can distinguish between the two by stress at proper places and gestures.

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1  
But pragmatically, the exclusive reading is pretty well impossible with general terms like "positive numbers". With specific terms like "a positive number or a negative number", on the other hand, the exclusive reading is almost forced. –  Colin Fine May 25 '11 at 14:18
    
I don't understand your syntax X is equivalent to Y,X. What is that? –  xport Jun 10 '11 at 14:58

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