Step 1: Bauxite ore is primarily composed of aluminum oxide (\( {Al}_2{O}_3 \)) and is contaminated with other oxides such as silica (\( {SiO}_2 \)) and iron oxide (\( {Fe}_2{O}_3 \)).
Step 2: The element X in the question is silica, which is a non-metal and belongs to the third period. Element Y is iron, a metal, and belongs to the fourth period.
Step 3: The oxide of silicon (\( {SiO}_2 \)) has a three-dimensional polymeric structure due to the network of strong covalent bonds between silicon and oxygen atoms.
Step 4: Therefore, both statements (a) and (B) are correct.