Let F be a finite field if

f:F-->F given by f(x)=x^3 is a ring homomorphim THEN WITCH IS TRUE AND WHY

1)F=Z/3Z

2)F=Z/2Z or characteristic of F=3

3)F=Z/3Z or F=Z/2Z

4)characteristic of F=3

next question

let E be set of all rationals p such that 2< p^2< 3 then E is

1)compact in Q

2)not compact in Q

3)closed and bounded in Q

4))closed and unbounded in Q

please also give reasons thanks