We are given that $P(A) = P(B) = 1/2$ and $P(A \cup B)= 2/3$.
I found that events $A$ and $B$ are not mutually exclusive by showing that $P(A \cup B) \neq P(A) + P(B)$ (i.e. $2/3 \neq 1$)
I also found that the two events are not independent by showing that $P(A \cap B) \neq P(A)P(B)$ (i.e. $1/3 \neq 1/4$)
Because the events are not mutually exclusive or independent I am having trouble solving for $P(A'\cap B)$ and $P(A' \cap B')$. I wanted to use the fact that $P(A'\cap B) = P(B) - P(A\cap B)$ but the events must be mutually exclusive to use this.