If $A$ and $B$ are two events such that $P(\overline{A} \cup \overline{B}) = \dfrac{2}{3}$ and $P(A \cup B) = \dfrac{5}{9}$, then which of the following are TRUE?

A. $P(A \cap B) = \dfrac{1}{3}$

B. $P(A \cup B) + P(A \cap B) = \dfrac{7}{9}$

C. $P(A) + P(B) = \dfrac{2}{9}$

D. $P(\overline{A}) + P(\overline{B}) = \dfrac{10}{9}$

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