Dear NT:

You wrote:

Are sentences “1” and “2” both acceptable in this context:

You said that your cousin was in the house. We went there, and there was nobody in the house.

1-I said my cousin lived there. I didn’t say SOMEBODY was there.
2-I said my cousin lived there. I didn’t say ANYBODY was there.

Both make sense. Normally “any” goes with a negative, so most English speakers would say #2. Sentence #1 is a little ambiguous because somebody does live there. “Anybody” or “anyone” is more standard and what would normally be said.