Step 1: Understanding the Concept:
Covalency refers to the number of electron pairs shared by an atom. Oxygen belongs to the 2nd period and lacks d-orbitals, which limits its maximum covalency. Oxidation states are determined by electronegativity differences.
Step 2: Key Formula or Approach:
1. Check oxygen's covalency limits (Valence shell is $n=2$, orbitals available: $2s, 2p$).
2. Compare electronegativities of O, S, and F.
Step 3: Detailed Explanation:
1. Statement I analysis: Oxygen has only four valence orbitals ($2s$ and three $2p$). Due to the absence of d-orbitals, its covalency rarely exceeds 2 and cannot exceed 4 (it is usually limited to 3 in hydronium ions, $H_3O^+$). However, Statement I says it "can exceed up to four," which is incorrect. Oxidation states are correct (O is -2 in $SO_2$ and +2 in $OF_2$ because F is more electronegative). Since part of the statement is wrong, Statement I is false.
2. Statement II analysis: Oxygen shows anomalous behavior (like being a gas $O_2$ while others are solids, and forming H-bonds) strictly due to its high electronegativity, small size, and absence of d-orbitals. This is true.
Step 4: Final Answer:
Statement I is false, but Statement II is true.