Let's analyze the statements based on chemical properties and thermodynamics:
Analysis of Statement I:
Electropositivity is essentially the opposite of electronegativity; it reflects how easily an atom can become a cation. In electrochemistry, we use reduction potentials to compare this. A highly negative reduction potential means the element is a strong reducing agent and is easily oxidized.
The standard reduction potential for Aluminium ($Al^{3+} + 3e^- \rightarrow Al$) is $-1.66\text{ V}$, which is quite negative.
The standard reduction potential for Thallium ($Tl^{3+} + 3e^- \rightarrow Tl$) is $+1.26\text{ V}$.
Because Aluminium has a much more negative potential, it is far more prone to losing electrons than Thallium is to form a tripositive ion. This makes Aluminium more electropositive. Statement I is true.
Analysis of Statement II:
The ability of a metal to form ionic compounds depends on whether the energy released during compound formation (lattice or hydration energy) can 'pay back' the energy spent to ionize the atom.
For Boron, the energy required to remove three electrons is so high due to its small size and high effective nuclear charge that it is almost never recovered. Therefore, Boron prefers to share electrons, leading to the formation of covalent compounds.
For Aluminium, the atomic radius is larger and the sum of ionization enthalpies is significantly lower. This energy requirement can be met by the lattice energy of ionic solids or the hydration energy in water, allowing the formation of the $Al^{3+}$ ion. Statement II is true.
Both statements are found to be correct upon verification with experimental data.