Suppose two events A and B are independent. (a) Is it true that A is independent of

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Suppose two events A and B are independent.
(a) Is it true that A is independent of B̅? If yes, give a convincing proof, otherwise, give a counterexample.
(b) Is it true that Ā is independent of B̅? If yes, give a convincing proof, otherwise, give a counterexample.
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