Cobra and new offered insrance

ody Q: I am on Cobra and was offered insurance from my new employer. I wanted to stay on Cobra but was told that I could not because of my new employer’s offer of new insurance. So I went ahead and signed up for the new insurance. Now I am being told that I could have refused the new insurance and kept my cobra insurance. My new insurance took effect on Nov.1st but I had already paid my Cobra for the month of November and there is an overlap. Is it legal for me to cancel my new coverage and continue to pay the Cobra? Also, because of the overlap am I liable for any services received from the Cobra insurance during the month of November?

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