$[20$ points$]$ Let A$1,$ A$2,...,$ An be a collection of sets. Prove the generalized DeMorgan$$s laws:

$[$n

i$=1$

Ai

$!$c

$=$

i$=1$

A

c

i

and

i$=1$

Ai

$!$c

$=$

$[$n

i$=1$

A

c

i