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.