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1. There is no place to have a beer.

2. There is nowhere to have a beer.

3. There is no room to have a beer.

Q1) Which ones are correct English?

I think only 3 is wrong and 3 should be "There is no room to have a beer in".

Q2) In 1,2,3, do "to have a beer" grammatically modify or describe "no place", "nowhere", "no room"?

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fire11. There is no place to have a beer.
2. There is nowhere to have a beer.
3. There is no room to have a beer.
Q1) Which ones are correct English?

(1) and (2) are OK. (3) is disrupted by the common expression "no room" meaning "not enough space" (e.g. a place is too crowded), rather than that a room does not exist.

fire1Q2) In 1,2,3, do "to have a beer" grammatically modify or describe "no place", "nowhere", "no room"?

It's tricky. "place to have a beer" could be replaced by, let's say, "bar", and we can say "There is no bar", which suggests that "to have a beer" modifies "place". On the other hand if "somewhere to have a beer" can be a phrase, which it can, then why not "nowhere to have a beer", and can't "no place" mean "nowhere"? Opinions may vary.

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fire1

1. There is no place to have a beer.

2. There is nowhere to have a beer.

3. There is no room to have a beer.

Q1) Which ones are correct English?

They're all correct. I take 'room' to mean 'space' in 3. Adding 'in' doesn't make sense.

fire1Q2) In 1,2,3, do "to have a beer" grammatically modify or describe "no place", "nowhere", "no room"?

Yes. I'd say "to have a beer" modifies the preceding noun phrase in all three cases. There is some overlap with the idea of "in order to have a beer" (infinitive of purpose), however, which others may see as more salient.

CJ

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Comments  
fire11. There is no place to have a beer.

This is more likely in American English.

fire12. There is nowhere to have a beer.

This is more likely in British English.

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CalifJimno place

AE speakers often use this and someplace when BE speakers often use nowhere or somewhere.