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I've always been lost as to how each differ from another as they all seem to mean can or to be able to.

Can someone clarify the differences and how each are used?

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    What do dictionaries say? Why isn't their answer sufficient? – user unknown Jan 7 '18 at 21:59
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können = can (I can do it)

dürfen = allowed to (I'm allowed to do it)

vermögen = capable (I'm capable of doing it)

During my last 3 years in Germany me and my colleagues didn't not use vermögen too much while communicating on a daily basis. But you can surely find it in official papers.

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dürfen doesn't fit in here - It means "to be allowed to".

können simply translates to "can" in all of its English meanings (both words go back to the same Germanic root) and denomainates a basic capability to do something.

vermögen basically means "can" as well, but with not quite so a wide range - you "kannst" do something, even if you don't want to. vermögen contains mögen, i.e. "to like", so its original meaning is more "can do what you like" than simply "be able to". The derived substantive Vermögen reflects that a bit in denominating your - financial mainly, but not only - assets. The Verb vermögen is a bit outdated these days and rarely used, the derived substantive is pretty common.

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