Should we say "und" or "oder" after "kein"?

Question

I'm currently taking A1.2. The question is what should we put after "aber"? Should we put "und" or "oder"?

Here is an example:

Aber wir haben kein Krankenhaus und kein Fitnessstudio.

Answer 1

I'm assuming you want to express that you don't have either. The meaning can in most cases be derived by logic.

"Wir haben kein A und kein B" means we have neither.

"Wir haben kein A oder kein B" means at least one is missing. You won't find such a statement outside a logic riddle.

"Wir haben kein A oder B" usually means "Wir haben kein (A oder B)", same as the first, we have neither.

"Wir haben kein A und B" is ambiguous. The literal meaning would be "B and not A", but most would understand it as short for "kein A und kein B".

Answer 2

The word »aber« is a conjunction (»nebenordnende Konjunktion« in German) which means it connects two main clauses. So, let's use it as it should be used:

Unsere Gemeinde hat 5.000 Einwohner, aber wir haben kein Krankenhaus und kein Fitnessstudio.
^{Our community has 5,000 residents, but we have no hospital and no gym.}

The part before »aber« is a full main clause that can stand alone as a sentence, and this is true for the clause following the word »aber«:

Unsere Gemeinde hat 5.000 Einwohner.
^{Our community has 5,000 residents.}
Wir haben kein Krankenhaus und kein Fitnessstudio.
^{We have no hospital and no gym.}

The second sentence is a complex sentence that is built from two two main clauses which contain identical parts of speech. Here are the two components as two separate sentences:

Wir haben kein Krankenhaus.
^{We have no hospital.}
Wir haben kein Fitnessstudio.
^{We have no gym.}

When you want to join both sentences as clauses of a longer sentence you need a joining conjunction, i.e. you need the word »und«:

Wir haben kein Krankenhaus und wir haben kein Fitnessstudio.
^{We have no hospital and we have no gym.}

Let's mark some other words in the same sentence:

Wir haben kein Krankenhaus und wir haben kein Fitnessstudio.
^{We have no hospital and we have no gym.}

The two main clauses share the same subject (»wir«) and the same Prädikat¹ (»haben«) and therefore you just need to use each of them once, which works exactly the same way as in English.

Wir haben kein Krankenhaus und kein Fitnessstudio.
^{We have no hospital and no gym.}

This is how this sentence is constructed, but when you have a closer look, you will find, that this construction is completely independent from the conjunction »aber«.

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To proof this, we can try to create a complex sentence where we need an or instead of an and. We begin with two separate sentences:

Thomas möchte das Bild in die Küche hängen.
^{Thomas wants to hang the picture in the kitchen.}
Thomas möchte das Bild in das Wohnzimmer hängen.
^{Thomas wants to hang the picture in the living room.}

But it's the very same picture. He can't hang it in both rooms at the same time, but he can hang it in one room or in the other room:

Thomas möchte das Bild in die Küche hängen oder Thomas möchte das Bild in das Wohnzimmer hängen.
^{Thomas wants to hang the picture in the kitchen or Thomas wants to hang the picture in the living room.}

Again we have a common subject (Thomas) and a common Prädikat (möchte ... hängen), and we even have a common Akkusativobjekt (das Bild):

Thomas möchte das Bild in die Küche hängen oder Thomas möchte das Bild in das Wohnzimmer hängen.
^{Thomas wants to hang the picture in the kitchen or Thomas wants to hang the picture in the living room.}

And now you can omit duplicates to make the sentence shorter:

Thomas möchte das Bild in die Küche oder in das Wohnzimmer hängen.
^{Thomas wants to hang the picture in the kitchen or in the living room.}

Now let's use this complex main clause as the second clause of a sentence that holds together two clauses with the conjunction aber. We begin with the two separate sentences:

Barbara hat das Bild für das Schlafzimmer gekauft.
^{Barbara bought the picture for the bedroom.}
Thomas möchte das Bild in die Küche oder in das Wohnzimmer hängen.
^{Thomas wants to hang the picture in the kitchen or in the living room.}

And now we join them together with the word aber:

Barbara hat das Bild für das Schlafzimmer gekauft, aber Thomas möchte das Bild in die Küche oder in das Wohnzimmer hängen.
^{Barbara bought the picture for the bedroom, but Thomas wants to hang the picture in the kitchen or in the living room.}

So, as you can see, the conjunction used in a complex main clause is completely independent from the word aber.

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¹ _{Note that in German grammar the predicate is defined different than in English grammar. In English it is everything but the subject, i.e. including all objects, while in German the Prädikat is just the set of all verbs plus so called Prädikativa, but this would lead too far away from your question. Here is just important, that »kein Krankenhaus«, »kein Fitnessstudio«, »das Bild«, »in die Küche« and »in das Wohnzimmer« are not part of a German Prädikat.}