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# Let R denotes the set of all real numbers and $R^{+}$ denote the set of all positive real numbers. For the subsets $A$ and $B$ of R define $f:A \to B$ by $f(x)=x^2$ for $x \in A$. Observe the two lists given below:

 List I List II (i) f is one-one and onto if (ii) f is one-one but not onto if  (iii) f is onto but not one-one if (iv) f is neither one-one nor onto if (a) $A=R^{+}, B=R$ (b) $A=B=R$ (c) $A=R,B=R^{+}$ (d) $A=B=R^{=}$

The correct matching of list I to List II is

(i)    (ii)    (iii)   (iv)

(1)  (a)  (b)   (c)    (d)

(2)  (d)  (b)   (a)    (c)

(3)  (d)  (a)   (c)    (b)

(4)   (d) (b)   (c)    (a)

(3)