1. ## Sets

If $A \subseteq B$, show that $P(A) \leq P(B)$.

So $B = A \cup (A' \cap B)$

And $P(A \cup B) = P(B)$, $P(A \cap B) = P(A)$, and $P(A) = P(B) - P(A' \cap B) = P(A \cup B) - P(A' \cap B)$.

Does this imply that $P(A) \leq P(B)$?

2. $0 \le P\left( {A' \cap B} \right)\; \Rightarrow \;P(A) \le P(A) + P\left( {A' \cap B} \right) = P(B)$