Math Help - proof

1. proof

Let
A1,A2, . . . ,An be subsets of . Show that if A1,A2, . . . ,An are independent, then the
same is true when any number of the sets
Ai are replaced by their complements (Ai)c. (Hint:
First do the case in which just one of the sets is replaced by its complement. Then argue by

induction on the number of sets replaced.)

2. Originally Posted by mathgeek
Let
A1,A2, . . . ,An be subsets of . Show that if A1,A2, . . . ,An are independent, then the

same is true when any number of the sets
Ai are replaced by their complements (Ai)c. (Hint:
First do the case in which just one of the sets is replaced by its complement. Then argue by

induction on the number of sets replaced.)