Step 1: Statement I - trans + Br2.
Anti-addition: Br2 adds from opposite faces. Trans-but-2-ene + Br2 → meso-2,3-dibromobutane. Statement I = correct.
Step 2: Statement II - cis + KMnO4.
Cold alkaline KMnO4: syn-hydroxylation. Cis-but-2-ene + KMnO4 → meso-butane-2,3-diol. Statement II = correct.
Step 3: Final.
\[ \boxed{\text{Both statements correct}} \]