Intersection and Union of two measurable sets

Question

need some help with the following problem in Measure Theory (couldn't find this on the forum)

Q. Prove that if A1 and A2 are measurable then

$$\lambda(A1 \bigcup A2) + \lambda(A1 \bigcap A2) = \lambda(A1) + \lambda(A2) $$

Answer 1

Hint. Let $C = A_1 \cap A_2, B_1 = A_1 \setminus C, B_2 = A_2 \setminus C$. Then $C, B_1, B_2$ are disjoint measurable sets. These sets have nice addition properties you can use.

Answer 2

$\lambda(A_1) + \lambda(A_2) = \lambda( A_1 \cap A_2 ) + [ \lambda(A_1 - A_2) + \lambda(A_2 - A_1) + \lambda (A_1 \cap A_2)] = \lambda (A_1 \cap A_2) + \lambda(A_1 \cup A_2) $

You can draw a vent diagram if you have a hard time to see this.