I am trying to prove the following:
If are mutually independent events, then
This is true for
by DeMorgan's Law
and since and are independent, and are independent
Therefore
Assume true for n
Then
Thus by the theorem for n=2
But by induction hypothesis
Thus
Which is what we want.
I was wondering if I proved the base case correctly and applied the induction hypothesis correctly. Thank you for your help.