Which of the following is the correct formal definition of two events being disjoint (mutually exclusive)?

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$A\cap B\in \varnothing$

$P\left(A\right)=P\left(B\right)$

$P(A\cap B)=P\left(A\right)\cdot P\left(B\right)$