No, they have different meaning. There are some cases where both åt and till work, this sentence is an example of this. I'm sorry but the difference between these three prepositions is one of the trickier parts of Swedish grammar so you can't expect to understand it all at once.
As the article explains, the core meanings are:
- till – recipient – you give something to someone
- åt – beneficiary – you do something so someone else doesn't have to
- för – audience – you show or tell something to someone
This is however very simplified, so there's much more to learn.
Does this make sense? Till - recipient: Jag köper en öl till dig.
Åt - beneficiary Jag dricker en öl åt dig.
För - Audience Jag dricker min öl för dig.
Is it all in correct context?
Yes, like others on these boards, the prepositions are very tricky. Sometimes I get them right and sometimes I don't. Unfortunately, the duolingo site doesn't seem to have any actual instructions, meaning that I'm literally left to guess; but at least they have a place where we can ask other users these questions.
Yeah, unless you have an object that you refer to. Then you replace mat by that word.
- Jag måste laga mat. = I have to cook.
- Vad ska du laga? = What are you going to cook? (Speaker expects an object to fill the void after laga here.)
- Jag ska laga pasta med köttfärsås. (I am going to cook pasta bolognese.)
If you just say laga it would mean ’mend’, like ”Jag måste laga min cykel.”
This is the most confusing for me (prepositions). I can't always know if I should use "for" or "at" or "till." Oh, and since I'm typing this in English, it doesn't allow me to use the Swedish way of writing these words. I'm also wondering if any of them are interchangeable (as they sometimes are in English):
I'm really trying to learn Swedish and therefore find it disconcerting that Duo doesn't correct my mistakes. Duo allows many small spelling errors to pass through the sieve, but that reinforces the tendency to keep on making the same errors. The example here is that I spelled "lagar" as "lager" and spelled "åt" as "ått". And I wasn¨t corrected and was going to zoom right on when I thought to stop and check it out for myself on Google Translate.