A couple induction set proofs

Prove the following statements

1) Prove: There is just one minimal induction set.

I know that there cannot be two minimal induction sets, but this says there does not exit zero minimal induction sets. I'm pretty sure that I have to use the definitions of propers subsets and subsets in there somewhere, I'm just not sure where it all fits in.

2) Prove: If C' is a subset of C, and C' is an induction set, then C' = C.

I haven't really gotten started on this one, but I know that an induction set is a set A such that 1 is an element of A and if x is in A, then x+1 is an element of A.

Thanks for any help you are able to provide