What is the difference between "Ingen" & "Inte"
When do we use each one? Examples please. Thank you.
You could look at "ingen" as a shorter form of "inte någon".
Ingen/Inga/Inget is translated to "no" in English, whereas inte is translated to "not".
I have no answer - Jag har inget svar (Jag har inte något svar)
They have no books - De har inga böcker (De har inte några böcker)
We have no cat - Vi har ingen katt (Vi har inte någon katt)
I do not have a house - Jag har inte ett hus
They do not have books - De har inte böcker
We do not have a cat - Vi har inte en katt
With verbs it's always "inte";
She does not run - Hon springer inte
Oh Cool! This is the first time I notice that! Through the whole "Rosetta Stone" swedish course, they always used the "inte något" form, I don't remember seeing the "inget" form there. Is the latter form something like less formal? Something you won't use in a formal letter or text?
I would say that it's rather a question of emphasis. If you really want to emphasize that you have none, you might prefer the longer version. But they are more or less interchangeable.
Might be interesting to know too that "någon" could be shortened to "nån", and "något" to "nåt".
So, "inte något", "inte nåt" and "inget" all mean the same.
If you're still interested, I've written a longer post about it in Swedish here: https://www.omsvenska.se/ingenting-eller-inte-n%C3%A5gonting/
There is also a quiz at the bottom, if you want to test yourself. :)