If `A,B` and `C` are mutually independent events then prove that `AuuB` and C are also independent

If A, B and C are mutually independent events, prove that the events (A cup B) and C are also independent events.

If E and F are two independent events then prove that E' and F' are also independent.

If E and F are two independent events then prove that E and F' are also independent events.

Pairwise and mutually independent events

If A^c and B^c are two independent events, then show that A and B are also independent.

If A and B are two independent events, prove that A^C and B are also independent events.

If A and B are two independent events, then Prove that A and B^' are independent events.

If A and B are independent events, then A' and B' are also independent.

If A and B are independent events, then A' and B' are also independent.

If A and B are independent events, then A' and B' are also independent.