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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.
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