Hello!
I have to put the verb in Present Perfect or Present Perfect Continuous: Sam (not talk) to us since he came.
To my mind both tenses are good with some difference in the meaning:
1. "Sam hasn't been talking to us since we came" - emphasizes the process of "not talking" during a period of time untill now, the action may still be going on.
2. "Sam hasn't talked to us since we came" - here we're speaking about the result "hasn't said a single word so far"
Am I right in my reasoning?
You're right. Both are possible.
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