I'm supposed to prove that if $A \subset B$, then $P(A) \leq P(B)$. The hint it gives is confusing me even more. It says use a venn diagram to convince yourself $ B = A \cup (A^c \cap B)$ and $A$ and $A^c \cap B$ are disjoint.
I know that I can do this:
$A \cup (A^c \cap B) = (A \cup A^c) \cap (A \cup B)$
Since $(A \cup A^c) = U$ that means if it intersects with $A \cup B$ we just have a venn diagram with everything shaded in.
How do I use this to my advantage to prove the original question? And wouldn't the two sets $A$ and $A^c \cap B$ being disjoint hurt me? Since I want to show that everything in $A$ is in $B$?