Statement I : Acid strength increases in the order given as HF << HCl << HBr << HI. Statement II : As the size of the elements F, Cl, Br, I increases down the group, the bond strength of HF, HCl, HBr and HI decreases and so the acid strength increases. In the light of the above statements, choose the correct answer from the options given below.

The correct option is Both Statement I and Statement II are true.

Let us analyze both statements step-by-step to understand the behavior of halogen acids (hydrohalic acids):

Analysis of Statement I:
Statement I states: "Acid strength increases in the order given as HF << HCl << HBr << HI."
The acid strength of hydracids of group 17 elements depends on their ability to donate a proton ($H^{+}$) in aqueous solution. Experimentally, HF is a weak acid, whereas HCl, HBr, and HI are strong acids. Among them, HI is the strongest acid because it dissociates most easily to release $H^{+}$ ions. Therefore, the order of acid strength is indeed:
$\mathrm{HF}<\mathrm{HCl}<\mathrm{HBr}<\mathrm{HI}$
Thus, Statement I is correct.

Analysis of Statement II:
Statement II states: "As the size of the elements F, Cl, Br, I increases down the group, the bond strength of HF, HCl, HBr and HI decreases and so the acid strength increases."
Going down the group from fluorine (F) to iodine (I), the atomic size of the halogen increases significantly: F < Cl < Br < I. As the size of the halogen atom increases, the overlap of its orbital with the small 1s orbital of hydrogen becomes less effective. This results in an increase in bond length and consequently a decrease in bond dissociation enthalpy (bond strength) in the order:
$\mathrm{H-F}>\mathrm{H-Cl}>\mathrm{H-Br}>\mathrm{H-I}$
Because the H-I bond is the weakest, it is cleaved most easily, allowing HI to release protons most readily. Hence, the acid strength increases down the group as the bond strength decreases. Therefore, Statement II is correct and provides the correct explanation for Statement I.

Consequently, both Statement I and Statement II are true.