6. Let A1, A2 A, be events, and let N denote the number of them that occur. Also, let 11 if all of these events occur, and let it be 0 otherwise.

Prove Bonferroni's inequality, namely that

$$

P(A_1 ...A_n) \ge \sum_{i=1}^{n} P(A_i) - (n - 1)

$$

HINT: Argue first that N-1+1.