Solution
= Solution
If $T_G\cap L_X$ is inconsistent for some finite $X\subseteq G$, then its superset $T_G$ is inconsistent. Together with parts (i) and (ii), this proves the equivalence of all three conditions.
= Solution
If $T_G\cap L_X$ is inconsistent for some finite $X\subseteq G$, then its superset $T_G$ is inconsistent. Together with parts (i) and (ii), this proves the equivalence of all three conditions.