Confirmation on probability identity I need a confirmation regarding a probability formula:

$ P(A\cup B)=P(A\cap B)+P({ A }^{ c }\cap B)+P(A\cap { B }^{ c }) $

I am asked if this identity is true.

For me, it is true.
Can you please confirm?

Thanks in advance.
Hint Draw a Venn diagram of the sets $A$ and $B$. Color the three sets $A \cap B$, $A^C \cap B$ and $A \cap B^C$. What do you get?
[sorry, didn't see the other answer, which says the same as mine]

if you have the decomposition of $A \cup B$ into three disjoint sets, then the result follows from the additivity of the probability measure. so can you prove that:
$$
A \cup B = A \cap B + A \cap B^c + A^c \cap B
$$
where the $+$ means disjoint union?