# Independence of complement Independence events

I need to show that if $E_1,E_2,\ldots, E_n$ are independent then $E_1^c ,E_2^c,\ldots, E_n^c$ are independent too. Please provide a hint.

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Possible duplicate – Stefan Hansen Jan 5 '13 at 9:18

Hint Use induction. Another hint for the basis ($n=2$):
Let $E_1,E_2$ independent. Then $E_1$ and $E_2^c$ are independent.
Applying this theorem you can easily prove the independence of $E_1^c$, $E_2^c$
(If you are done with $n=2$, I can add some more hints...)