Translation:Shall we run next week?
走りましょうか = shall we run?, and 走りませんか = won't we/you run? ('are we not running?')
In effect, both are about making a suggestion, albeit in question form. The main difference is that ～ましょうか implies a readiness or willingness from the speaker to undertake a certain activity, whereas ～ませんか is more about gauging the willingness of the listener.
ましょう is more closer to suggesting [ usually when the relationship is close and the listener would more likely to agree to the suggestion ], whereas ませんか would only be used as a form of invitation [ where the relationship is not so close and both speaker and listener knows it is totally ok to reject the invitation without feeling bad ]
How are we supposed to answer ませんか question in this case (are we not running?) with はい we are running or いえ we are running?
You should not use 「~ましょうか」 when talking to olders. You can use 「~ませんか」
Am I wrong?
It's mostly a technicality, but "should" implies a judgment rather than a suggestion. In English it would be understood, but there's another word ending that means "we should" or "we must" in Japanese that you'll learn later.
Yeah. "Shall" is like formal semi archaic English. I like to say shall but I'm not sure I have ever heard anyone other than my family use it.
I used "Shall we go running next week?" I would say it's a very friendly way to suggest something, which I think is a good way to translate this sentence. I wouldn't say it's wrong, it would depend on intonation at that point.
"Shall" is weird, it sounds perfectly natural to use it in a question, but if you said "I shall go running next week" it sounds really old-fashioned.
Yes, I think the only thing most Americans of my acquaintance would say that would translate this, though, would be something like "Do you want to go running next week?" I guess they might say "Should we go running next week?" if there were a real issue about it, e.g. snow was expected, one had a big final exam that week, etc. I don't think I have ever heard "shall" in this use without it being a sort of mocking formality.
Using 'let's' or 'shall we'.. doesn't make it a question.. Its still a request.. And i learned in an earlier sentence that mashou could mean either one.
I'm pretty sure the first one is the topic particle and the second one is the first letter in the verb.
I believe you can write it with or without, since you are referring to a time in the near future or past (someone back me up on this though)
It should be noted that "to run," はしる、is an exeption to the usual split of verbs. It should be a ichidan (ru-verb) but it is a godan (u-verb), despite ending in the いる or える sound.
How do we know the difference between "shall we..." and "shall i..." in this context?
It depends on the context. I can't really think of a context where it makes sense for you to ask someone else whether you yourself will run.
Is it typical to use the topic marker (wa) after the time word (raishuu)?
It's written in hiragana, not katakana. I don't really have a good answer for your actual question, but I think it has to do with the conjugation. 走る is another form of the same verb. Kanji wouldn't allow for that as well.
I wrote "shall I run next week." Marked incorrect. Is there something that indicates that the subject is 'we'?
Not native english speaker, what is the difference between Shall we run next week and Shall we run the next week [sorry if is a basic question]
No, it's a pretty complicated question, and it may be different in different English dialects. In my dialect of American English, "shall we run next week" is pretty common and refers to the week after the current one, e.g. seven or so days from now. The only situation in which I would say "shall we run the next week" would be if we were scheduling a run for some time in the future and I was talking about the week after a future week we had already talked about. E.g. "Let's run together four weeks from now. No, that doesn't really work for me. Well, shall we run the next week?"
As Steven said, that's not はは as in "mother." But I want to explain more generally: because Japanese has far, far fewer sounds than English (and no spaces between words when written down), there ends up being a lot of words/phrases that have the same sequence of sounds but aren't related at all. Often they'll be written differently (like in kanji, as opposed to spelt out in katakana/hiragana), or you can tell by context or the position in the sentence. Which may be confusing at first, but it'll get easier as you expand your vocabulary!
来週ははしりましょうか i wrote the exact answer and duolingo says i didn't write it right...
How do you determine this is "we" and not just asking someone if they will go running next week?
That is the meaning of the ～ましょうか ending. If it were a plain question, it would simply end in ますか.
It's correct, Duolingo just doesn't know to recognize the kanji. Report things like that please.