Probability with Multiple Sets and Anti Sets

Question

Calculate: $P(A \cap B'\cap C')$

Given:

• $P(A) = 0.7$
• $P(B) = 0.8$
• $P(C) = 0.75$
• $P(A \cup B) = 0.85$
• $P(A \cup C) = 0.9$
• $P(B \cup C) = 0.95$
• $P(A \cup B \cup C) = 0.98$

I can upload a pic of my work so far (in which I attempt to break down the formulas to it's elementary forms), but I keep getting to a step which I cannot move on from.

Answer 1

$$ A\cap B'\cap C'=(A\cup B\cup C) - (B\cup C) $$

where

$$ B\cup C \subseteq A\cup B\cup C $$

Now can you answer by yourself?

Answer 2

Prove $$A \cap B'\cap C' = A \setminus [(A \cup B) \setminus (A \cup B \cup C)] \setminus [(A \cup C) \setminus (A \cup B \cup C)]\setminus (A \cup B \cup C)$$ and use it to find the answer!