Does 'some' necessarily imply 'not all'?
If some X's are Y's, does that imply that some X's are not Y's?
This is bordering on logic rather than language, but the answer is definitely no: Some is "an indeterminate amount", which means it can be all. If I say I have some red M&Ms in my bag, it could be that all of them are red.
But then, depending on inflection, as @codelegant pointed out, I could be using emphasis on some to indicate that not all are red...like if you asked for some red ones and I said I had some, which turned out to be more than one but less than all.
Yes. If I offered you some peanut M & M's, I would feel that you misunderstood me if you took them all. :)
For straight English prose, yes. It implies more than one, but not all.
However, for a discrete math homework or test question, I think it would be synonymous with "one or more". It could be just one, or it could be all of them. So if you are asking this question to try to get a couple of points back from your math instructor, sorry. :-)
the answer is No.
b. Equipolence
Closely connected with the theory of opposition is that of the equipollence of propositions with the same terms in the same order but with negative particles variously placed within them. Since contraictories are true and false under reveresed conditions, any proposiltion may be equated with the simple denial of its contradictory. Thus, "Som X is not a Y" has the same logical force as "Not every X is a Y," and vconversely, "Every X is a Y" has the force of "Not (some X is not a Y)," or, to give it a more normal English expression, "Not any X is not a Y". Similarly, "Some X is a Y" has the force of "Not (no X is a Y)" and "No X is a Y" that of "Not (some X is a Y)" -- i.e. "Not any X is a Y." Also, since "no" conveys universality and negativeness at once, "No X is a Y" has the force of "Every X is not-a-Y", and, conversely, "Every X is a Y" has the force of "No X is not-a-Y." Writers with an interest in simplification have seen in these equivalences a means of dispensing with all but one of the signs "every", "Some", and "no." thus the four forms may all be expressed in terms of "every", as follows:
Every X is a Y (A)
Every X is not-a-Y (E)
Not every X is not-a-Y (I)
Not every X is a Y (O)
(emphasis in bold is mine)