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Hi,
Which ones show positive and negative polarity properly for the uses of the words 'a few' and 'few'? Which ones are not necessary?

1,After a few (few -- necessary??) exhausting days of workouts, I took a long rest at home.
2.Few (IMO, A few is good if you want to create that polarity effect) excruciating workouts can do a work on your body.
3. He should drink few (a few is good, IMO, if you intend to say something to the opposite effect) cups of water when he works out strenuously.

But no. 1 is where a person would not normally resort to positive- or negative-polarity notion use. Can you think of few (a few ??) more uses like this?
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As you say, "a few" is positive ("not many, but some"), and "few" is negative ("hardly any", "not as many as expected"). I don't really understand what you mean by "Which ones are not necessary?", but anyway...

"Few" is very unnatural in (1). It's not something anyone would ever want to say because the "hardly any" meaning does not fit with the rest of the sentence. "A few" is fine.

In (2), "can do a work on your body" is not grammatically correct, and the extent to which "few" and "a few" both work depends on what you are trying to say here (which isn't clear to me).

In (3), "few" is possible but unlikely. If you wanted the "few" meaning then normally you would say something like "He shouldn't drink very/so many cups...". "A few" is natural here (but, of course, has a different meaning).
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1,After a few exhausting days of workouts, I took a long rest at home.
2.Few (IMO, A few is good if you want to create that polarity effect) excruciating workouts can do a work on your body. Incomprehensible. I can't help you here.
3. He should drink a few cups of water (every two hours) when he works out strenuously.
There's no such thing as "creating a polarity effect". "a few" has positive polarity; "few" has negative polarity; end of story.
a few = a small number of
few = not many
Please see a few more
CJ