Could you do a lesson on 겠지 and 아니겠지 when used as a question and as a statement?
There are a lot of grammar points in here, so I'll give you an index:
-겠다; intention, will / observation, supposition
-지(요)/죠?; right?, isn't it?
I sincerely apologize for the length of this post! There's a lot to unpack in just those two phrases, so I hope this helps.
1. -겠다; intention, will (1) / observation, supposition (2)
Phrases you’ll hear/know using -겠다:
(1) 잘 먹겠습니다 – I’ll eat well (aka: I intend to eat well)
(1) 뭐 드시겠습니까? – What will you eat? (높임말)
(1) 잘 하겠습니다 – I’ll do my best!
(2) 맛있겠습니다! – I suppose it is delicious
(2) 피곤하겠습니다 – I suppose you're tired
(2) 내일 비가 오겠습니다! - I suppose it's going to rain tomorrow
Use it for yourself when you want to express first-person intent or will
If you do this, then remember that it’s more common and natural to use -겠다 with formal grammatical patterns (that’s why you see -(스)ㅂ니다 in all the examples)
This pattern also puts more emphasis on the intention than the simpler (으)ㄹ 것이다 future tense; if you use the -겠다 pattern, you mean it, essentially.
Use it when you want to make an observation towards someone or something else
Use it when inquiring about another person’s intent or will
All that said, you can use -(으)ㄹ 것이다 to express a future action in a less formal situation.
뭐 먹을 거야? (with friends) vs. 뭐 드시겠습니까? (as the server)
Note: you can use this pattern in lower formality situations (as an example, 힘들겠어; it seems difficult), it's completely okay! It's just more common to use -겠습니다 when talking about the intended future in a formal situation.
2. -지(요)/죠; right(?), isn't it?
This is used to ask for confirmation from the speaker about an observation! For us Canadians, this is the "eh?" we love so dearly. You can use this as a statement, to agree with the speaker. The difference between 지요 and 죠 is just pronunciation; they're the exact same thing. Examples:
춥죠? - it's cold, isn't it? (Canadian translation: it's cold, eh?)
외국인들은 한국에서 일하기 힘들지요? - it's hard for foreigners to work in Korea, right?
알고 있죠? - you know that, right?
당근이지 - right, of course! (informal)
This is pretty self-explanatory. It's the opposite of 이다! When using this verb, make sure you use 이/가 particles! Here are some examples:
그 남자는 배우가 아니에요 - he's not an actor
학생이 아녜요! - I'm not a student
부자가 아니에요? - you're not rich?
If we combine 아니다 and 지요 we can get sentences that express a negative statement to be confirmed. It's best to illustrate this with examples:
농담이 아니죠? - you're not joking, right?
부자가 아니지요? - you're not rich, are you?
한국인이 아니죠? - you're not Korean, right?
Note: when answering these questions, you have to answer the Korean way; we have to think of if we agree or disagree with the statement. Look here for examples.
Final grammar point! This is also pretty self-explanatory. As we know, -겠다 is used to express an observation or supposition. When we attach -지요, we are expressing that we need the listener to agree with our future observation. Examples:
쉽겠죠? - I suppose it's gonna be easy, right?
다음 주에 한국어 시험을 어렵겠죠? - The Korean test next week will be hard, right?
When adding 아니다 to 겠지(요)/죠, we are expressing a statement that we (the speaker) believe is a true observation.
코로나 때문에 한국에 가는 게 아니겠죠? - you aren't going to Korea because of CoVid, right?
감기에 걸렸기 때문에 학교에 오는 게 아니었겠지요? - you didn't come to school because you caught a cold, right?
If you disagree with these statements, you are more than welcome to say so. The question/statement is just an observation that the speaker believes to be true. For example, you could say:
A: 코로나 때문에 한국에 가는 게 아니겠죠?
B: 아니요, 돈이 없어서 한국에 못 가거든요 - No (I disagree that it's because of CoVid), I can't go because I don't have money.
You can use this when you want to express the hopefulness of something. The literal translation is "it would be good if~". Here are some examples:
한국에 가면 좋겠어요 - I hope to go to Korea
잘됐으면 좋겠어요 - I hope it goes well
상을 타면 좋겠어요 - I hope I win a prize/award
Ooof!! Finally at the end! Hope this answered your question! As always, if there's anything that you still don't understand, you're more than welcome to send me a pm and we can sort it out together!