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In many cases, yes, but not in general. Verhältnis can also be a love affair, an old fashioned tête-à-tête, then it's not interchangable. Verhältnis can also be a ratio, percentage, quotient. Generally spoken, a 'Verhältnis' can also describe how things act with or relate to each other. Beziehung is something social, a relationship, contact, tie or connection.
Usually kennen is concerning to people and countries Ich kenne deine Schwester Wir kennen Peter Kennen Sie París ? And Wissen refers to facts,knowledge and how to do something Ich weiß,dass die neue mathematische Formel I konw the new mathematical formula
Weist du wie man schwimmen /fährt? Do you know how to swim/drive?
I hope that helps
No, they are in no way interchangeable. Kennen means to know "of/about" something/someone, whereas wissen is that you know a specific thing.
Kennst du ihn? --> Do you know him? Weißt du, wie spät es ist? --> Do you know how late it is?
It's a similar system to Spanish I've heard.
I'm not sure about general usage in Germany, but my Austrian wife overheard me practising on Duolingo and pointed out that, to her knowledge, this word is exclusively used to describe an extramarital affair and so should not be used to translate 'relationship' when describing a marriage.
I can confirm this (I'm german).
"Wir haben ein Verhältnis." is equivalent to "Wir haben eine Affäre." and both are the confession of an extramarital relationship kept secret until then. "Das Verhältnis" is commonly understood in this context. It is specified if it is meant to be some other kind of relationship. Thus you may encounter expressions such as "freundschaftliches Verhältnis", "verwandtschaftliches Verhältnis" or "kollegiales Verhältnis".
The only cases I know in which "Verhältnis" has a neutral / general meaning is the question: "In welchem Verhältnis stehen Sie (zueinander)?" (=> What's your relationship (to each other)?") asked by a policeman, for example. Or if you kind of rate it like "Ich habe ein gutes Verhältnis zu meinen Eltern." (I have a good relationship with my parents.) already implying that the relationship is a parents-child-relationship and nothing sexually or similar.
Thought the same, but turns out that "behaviour" is actually being translated a "das Verhalten", not "das Verhältnis". So far I have thought they had the same meaning, but they obviously don't.
As for the verb "to behave", it can be translated as "sich verhalten". I suppose that is where the noun "das Verhalten" for "behaviour" comes from.