Normal subgroup interset Sylow subgroup

This question is bit long but please help me:

1.Let $N \triangleleft G$, where $G$ is finite group and $P$ be Sylow subgroup of $G$. Show $P \cap N$ is Sylow p-subgroup of $N$.

Let $|G|=p^ar$ $|N|=p^bs$ , $(r,p)=(s,p)=1$, $a \geq b$. And I think $|PN|= \frac{|P||N|}{|P \cap N|}$ have something to do with this question, but I have no idea.

2.Consider Sylow 2-subgroups $S_3$. Show if $P$ is Sylow p-subgroup of $G$ then $P \cap N$ is not Sylow p-subgroup of $N$ if $N \ntriangleleft G$.

Don't know how to do it at all, please help

Thank you.