Question: If A and B are both mutually exclusive and independent, then at least one of P(A) or P(B) must be zero. Assume A and B

If A and B are both mutually exclusive and independent, then at least one of P(A) or P(B) must be zero.

Assume A and B are events such that 0 < P(A) < 1 and 0 < P(B) < 1.

Is this true or false?

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