All five sentences are grammatically correct. Sentences #3 and #4 are the trickiest.
These two sentences are perfectly idiomatic:
. 2. Do you have something to eat?
. 5. She lived to be ninety.
Sentence 5 implies that "she" is dead. "She's ninety" or "She has lived to be ninety" or "She's looking forward to her ninety-first birthday in June" are things people might say if "she" is still alive.
The remaining three sentences start with an idiomatic sentence. They add a detail, in a grammatically correct way:
- It is fun to talk with foreigners.
This sentence combines "It is fun to <infinitive verb>" with an adverbial phrase that provides an indirect object.
- This is a deep lake to swim.
This sentence combines "This is a dangerous thing to do" with "This is a deep lake", "This is a place to swim", and "Some people can swim across this lake". You can imagine this sentence being built up in the following steps:
- "This is a dangerous river crossing."
- "It is dangerous to ford this river."
- "This is a dangerous river to ford."
- "This is a deep river to swim."
- "This is a deep lake to swim."
- She must be warm-hearted to help you.
This sentence combines "She must be nice." with "She went out of her way to help you", "She was happy to help you", and "Only a very nice person would help you." It substitutes "warm-hearted" for "very nice".
Notice the difference between:
She must be nice.
She must be a nice person.
Changing the predicate from an adjective to a noun phrase requires adding a determiner (such as the indefinite article "a").
Also notice the difference between:
She must be {very nice / warm-hearted} to help you.
and
{She must be glad / It must warm her heart} to help you.
The first pair of choices say that "We know that she is a very nice person, because only a very nice person would help you." The second pair of choices say that "Helping you makes her feel good."
1All of those sentences are grammatical. – Andrew Leach – 2015-12-24T17:44:10.823
3#3 is an odd duck semantically. It does not quite follow the "This is a hard problem to solve" pattern, or the "This is a fast road to take" pattern. Changing deep to cold would work better, for example. – Tᴚoɯɐuo – 2015-12-24T18:00:40.387
1But it's possible to understand it to mean, "Are we sure we want to swim in this lake? It's really deep." – Tᴚoɯɐuo – 2015-12-24T18:06:08.053
2Hey is this a trick question? The only ungrammatical sentence I see here is your title. :) – M.A.R. – 2015-12-24T18:29:25.987
hahaha, could you edit my title? I don't know what I am missing. – inches – 2015-12-24T18:47:39.640
@inches I did it for you. – Alejandro – 2015-12-24T18:57:22.733
23 is not incorrect, but weird, because
swim a lake
would more easily mean crossing it swimming, and the depth is hardly relevant.a wide lake to swim
would work better. – njzk2 – 2015-12-24T19:32:00.937I'd never use
swim
without "across" or "in" after it. What sort of English are you learning? – Azor Ahai -- he him – 2015-12-24T20:49:28.983@Azor-Ahai - I've seen "swim the Atlantic" or "swim the river" or similar plenty of times. For example, "What it's really like to swim the English Channel".
– stangdon – 2015-12-24T23:42:10.107As elaborated on in some answers below, that use is usually tied to something with a known crossing, like the the English Channel. I'd consider it idiomatic in that sense. I've never seen it in conjunction with some unnamed river, so I was wondering if maybe it was a British thing. – Azor Ahai -- he him – 2015-12-24T23:50:38.207