Does the independent event satisfy the probability addition formula

For example, a and B are two independent events, but a and B may occur at the same time; if a and B are mutually exclusive events, a and B cannot occur at the same time; if a occurs, B does not occur; if a does not occur, B must occur
The reason is as follows:
P(A+B)=P(A)+P(B)-P(AB)
P (a + b) = P (a) + P (b) only when p (AB) = 0, i.e. a and B cannot occur at the same time

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