Induction of Complementary Sets

Main Question or Discussion Point

I'm just wondering how induction can be used to show the following:

$$(A_1 \bigcup A_2 \bigcup A_3 \bigcup \cdots \bigcup A_n)^c = A^c_1 \bigcap A^c_2 \bigcap A^c_3 \bigcap \cdots \bigcap A^c_n$$