Consider \( ([0, 1], T_1) \), where \( T_1 \) is the subspace topology induced by the Euclidean topology on \( \mathbb{R} \), and let \( T_2 \) be any topology on \( [0, 1] \). Consider the following statements:
P: If \( T_1 \) is a proper subset of \( T_2 \), then \( ([0, 1], T_2) \) is not compact.
Q: If \( T_2 \) is a proper subset of \( T_1 \), then \( ([0, 1], T_2) \) is not Hausdorff.
Then, which of the following statements is TRUE?