P (A+B)= P( A)+ P (B) is not satisfied, because event AB may occur at the same time, and P (A+B) indicates that there is an event in AB.

P (A+b) = p (a)+P (B)-p (a ∧ b) is equivalent to P (A ∪B) (because P (A) and P (B) are added twice at the same time, they should be subtracted once).

P (A ∧B) indicates the probability of simultaneous occurrence of AB.

P ( A ∧B )=P( A)× P (B)

Mutually exclusive events said that two things didn't happen at the same time.

Satisfying P (A+B)= P( A)+ P (B) is equivalent to P (A ∪B).

P ( A ∧B)=0