1. Mind your own business.

2. Be careful of/about your own business.
3. Take care of your own business.
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Does #1 mean #2 or #3?

4. Do you mind if I open the window?
5. Do you feel annoyed if I open the window?
6. Do you opposed to me if I open the window?
7. Do you dislike if I open the window?
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In #4, what is the meaning of 'mind'?
Are the other sentences grammatical? Which one is similar to #4?

1 could mean 3, but only if 1 weren't said in an angry way. Usually, 1 is a forceful way to tell someone to back off!

Re #4 -- I wouldn't use 5, 6, or 7 to replace 4. I might say, "Would you be annoyed... " or "Are you opposed to my opening the window?" But these are not direct rephrasings of #4.

http://www.dictionary.com/browse/mind?s=t
Scroll down to the Verb meanings and check out the different uses. There are many because this verb is used in idioms, and you know that idioms are very difficult or even impossible to duplicate.

In #1, "Mind your own business" means to focus on and take care of your own affairs and not interfere in other people's matters. It implies that you should not meddle or pry into other people's lives.

Regarding #2 and #3, both convey a similar idea, but there might be a slight difference in nuance.

#2 "Be careful of/about your own business" suggests being cautious and mindful of your own affairs, possibly to avoid any negative consequences or interference from others.

#3 "Take care of your own business" implies that you should prioritize attending to your own matters, ensuring they are managed properly before concerning yourself with others.

Now, onto the second set of questions:

In #4, "mind" means "to care, to object, or to be bothered by" something. So when someone asks, "Do you mind if I open the window?", they are asking if it would be a problem or if you would object if they were to open the window.

Concerning the other sentences:
- #5 "Do you feel annoyed if I open the window?" is grammatically correct and asks if opening the window would cause annoyance to the person being asked.
- #6 "Do you opposed to me if I open the window?" is not grammatically correct. It should be "Do you oppose me if I open the window?" This asks if the person being asked is against the idea of the window being opened.
- #7 "Do you dislike if I open the window?" is not grammatically correct either. It should be "Do you dislike it if I open the window?" This asks if the person being asked has a negative feeling towards the window being opened.

#4 and #5 share a similar meaning and are grammatically correct. They both ask if the person would have any objection or be bothered if the window is opened.