2.3 Exercise 7

Suppose $P \left(\left(A B^{c} \cup A^{c} B\right)C\right) = 0 . 4 , P \left(A B\right) = 0 . 2 , P \left(A^{c} C^{c}\right) = 0 . 3 , P \left(A\right) = 0 . 6 ,$$P \left(C\right) = 0 . 5 ,$ and $P \left(A B^{c} C^{c}\right) = 0 . 1$. Determine $P \left(A^{c} C^{c} \cup A C\right)$, $P \left(\left(A B^{c} \cup A^{c}\right)C^{c}\right)$, and $P \left(A^{c} \left(B \cup C^{c}\right)\right)$, if possible.