A few proofs I need help with to get started...

I'm really quite distraught on two particular questions... I have attempted them, but I am new at proofs and help / ideas as to how to start these two proofs would be greatly appreciated! Thank you in advance!!

**Prove that the only set in R1 which is open and closed are the empty set and R1 itself.**

**Given a set S in Rn with the property that for any x that is an element of S ****there is an n-ball B(x) such that B(x)****S is countable. Prove that S is countable.**