I still have a few doubts on the use of infinitive and gerund. I hope you can check these sentences, too.
1)It took a lot of time for Jane to arrive.(is it wrong to say "It took Jane a lot of time to arrive?")
2) Why not go to the theatre, instead?
(Is it the same as: Why don't we go to the theatre..?)
3) I found my sister reading my diary. (Is "find" always followed by the gerund')
4) On passing by his bedroom I saw him studying. (Does it mean "When I passed by...?)
5) Why don't you try eating less? You might feel better.
He proposed (he meant, he intended) to rent a car, but then he changed his mind.
6) I hope to have finished this book by next week. (Is it the same as "I hope I'll finish this book..)
7) Having missed the bus, he arrived to school quite late. (= As/since he had missed the bus,....)
8) I'm worried about Brian's/Brian working so hard. I don't mind his/him going out after dinner. (Both possible??)
9) They encouraged/recommended/proposed/advised/suggested taking the motorway. (all possible?)
The don't allow/permit playing in the park.
1. Either phrasing works fine.
2. Both are fine, but they are not exactly alike in meaning.
3. Not always.
4. Yes, they both mean the same thing.
5-7 and 9. All variations are fine.
8. ... Brian's working... (Brian working is incorrect)
http://grammar.ccc.commnet.edu/grammar/gerunds.htm#possessive
1) Both sentences are grammatically correct, but they have slightly different meanings. In the first sentence, "It took a lot of time for Jane to arrive," the emphasis is on the amount of time it took for Jane to arrive. In the second sentence, "It took Jane a lot of time to arrive," the emphasis is on Jane and the fact that it took her a long time to arrive.
2) "Why not go to the theatre, instead?" and "Why don't we go to the theatre?" are similar in meaning but have different tones. "Why not go to the theatre, instead?" suggests that going to the theatre is a better alternative to something else, while "Why don't we go to the theatre?" simply suggests going to the theatre as an option. The first sentence seems to contrast two different options, whereas the second sentence is a straightforward suggestion.
3) In the sentence "I found my sister reading my diary," the verb "find" is followed by a gerund (-ing form). However, it is important to note that not all uses of "find" require a gerund. For example, you can also say "I found my sister in the kitchen" or "I found a pen on the table."
4) Yes, "On passing by his bedroom I saw him studying" can be understood to mean "When I passed by his bedroom, I saw him studying." The gerund "passing" serves as a way to describe the action at the same time as the main action of seeing him studying.
5) "I hope to have finished this book by next week" and "I hope I'll finish this book" have similar meanings, but there is a slight difference in emphasis. The first sentence emphasizes the completion of the book by a specific time ("by next week"), while the second sentence simply expresses a general hope to finish the book without mentioning a specific time frame.
6) "Having missed the bus, he arrived at school quite late" can indeed be understood as "As/Since he had missed the bus, he arrived at school quite late." The use of the participle phrase "having missed the bus" introduces a causal relationship between missing the bus and his arrival time.
7) Both "I'm worried about Brian's working so hard" and "I'm worried about Brian working so hard" are grammatically correct. The first sentence uses a possessive noun ("Brian's") and the gerund form ("working"), while the second sentence uses the objective pronoun ("Brian") and the gerund form ("working"). Both forms are acceptable, but the possessive form emphasizes Brian's ownership or involvement in the action more than the objective form.
8) All the verbs "encouraged," "recommended," "proposed," "advised," and "suggested" can be followed by the gerund form (-ing) or the base form of the verb. Therefore, all the following options are correct: "They encouraged taking the motorway," "They recommended taking the motorway," "They proposed taking the motorway," "They advised taking the motorway," and "They suggested taking the motorway."
9) The correct form is "They don't allow/permit playing in the park." Both "allow" and "permit" are followed by the gerund form (-ing) of the verb when expressing permission. So, it would be incorrect to say "They don't allow/permit to play in the park."