Hello,

I am confused with the following question.

Suppose are events, then

The right hand side is Boole's inequality. Prove the left hand side.

I am trying to prove this using induction, but I am not sure if I am doing it correctly.

For ,

Let and be events,

then, .

Thus, this holds true for .

Am I going on the right track?

Any suggestion for the inductive step?

Thanks in advance,