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## Main Question or Discussion Point

Theorem:

If P(A) = 1, P(B) = 1, then P(AB) = 1

My book starts out with the proof as follows:

P(A U B) >= P(A) = 1, so P(A U B) = 1

How do they reach such a conclusion?

Things I know:

P(A U B) = P(A) + P(B) - P(AB)

How can I use that to be sure that P(A U B) = 1?

If P(A) = 1, P(B) = 1, then P(AB) = 1

My book starts out with the proof as follows:

P(A U B) >= P(A) = 1, so P(A U B) = 1

How do they reach such a conclusion?

Things I know:

P(A U B) = P(A) + P(B) - P(AB)

How can I use that to be sure that P(A U B) = 1?