Property of the characteristic function for events

Question

We got to show the following equality:

$1_{A_1 \cup...\cup A_n} = 1 - \prod \limits_{i=1}^n (1 - 1_{A_i})$

First I would like to ask for hints for how to proove this equation (no solution though, I would like to solve it myself). Secondly I was wondering if there is an "intuitive" interpretation of this equality?

Answer 1

Yes. De Morgan's law for Boolean algebras:

$A\cup B=(A^c\cap B^c)^c$

where $X^c$ denotes the complement set. That's the hint.