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Thank you very much for so detailed answer. I would like to ask for one clarification: I played a little bit with my return by trying to see what will happen to it if I remove my child as dependent, once I did that - nothing was changed. This means that I just didn't have a child credit due to number of different reasons, am I right?
Now the main question: taking into account this info - do you think it still makes sense for me to specify my child on my return as dependent or not really?