I have an impression or feeling about how they seem to used, but I'm finding it hard to put into words. The closest I can get for now is that warum seems to be a general "why", while wieso seems to be used when you ask specifically asking for the cause of something.
So, I think we might use Wieso magst du Katzen? when you are (almost) asking "what happened to make you like cats?", if you see what I mean.
mcpolo's sentence is not correct.
The normal negation of the sentence "Ich mag Katzen"(=I like cats in general) is "Ich mag keine Katzen".(=I don't like cats.)
You say you want to negate "eine". The negation of "eine" is "keine". "not one" and "not a" is not "nicht ein/eine", it is "kein/keine".
I noticed that when watching a TV series. But they aren't close enough that I could get a good feel for most words.
There are many German words that are similar to words in many languages such as Swedish or Norwegian. I recently heard juice referred to as saft in Swedish, which sounded familiar, but then orange juice was called orange juice in the same show. So I looked it up and the translation called it apelsinjuice. So English helps a bit too.
As much as I would like to learn Dutch, it's hard to find Dutch speakers who don't already speak good English. I think knowing Dutch should give you a good head start.
Strictly speaking, ‘warum’ is for reason or motive, ‘wieso’ is for cause and ‘weshalb’ is for goals. But there are huge grey areas in between these and there is a strong preference for ‘warum’, especially at the start of a question.
So in current usage you might consider ‘warum’ unmarked, whereas ‘wieso’ and ‘weshalb’ are marked. And that may have led to the use of ‘wieso’ to express disbelief.
The authoritative Duden dictionary gives interchangeable and cross referencing definitions for the three words, although you can still see some difference in the listed usage examples.
Yes! In regular declarative sentences the verb always comes second. Ich mag Katzen. Forming questions is a bit different. There are two types of questions: yes and no questions and questions with a "question word."
In a yes or no question the verb comes first: Magst du Katzen?
Questions with a "question word" the verb again becomes second because the question word is in first position. Questions words are warum,was, wann, wo and etc. Warum magst du Katzen? Hope this is helpful!
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No, your first comment "Ich mag Katzen nicht, obwohl ich Hunde liebe" is much better than your correction "Mag ich Katzen nicht, obwohl ich Hunde liebe".
Ich mag keine Katzen, obwohl ich Hunde liebe. is the normal german sentence.
Obwohl ich Hunde liebe, mag ich keine Katzen. is the correct sentence if you change the position of the subordinated clause. Because here the subordinated clause takes the first position of the main clause, the main clause's verb is in the second position.