Let $A=\{x^2:0<x<1 \}$ and $B=\{x^3:1<x<2 \}$. Which of the following statement is true?
1.  There is one to one, onto function from $A$ to $B$.
2. There is no one to one and onto function from $A$ to $B$ taking rationals to rationals
3. There is no one to one from $A$ to $B$ which is onto.
4. There is no onto function from $A$ to $B$ which is one to one.