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

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

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

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