- \( \left( U_{1} \bigoplus U_{2} \right) \cap \left( W_{1} \bigoplus W_{2} \right) = \left( U_{1} \cap W_{1} \right) \bigoplus \left( U_{2} \cap W_{2} \right) \)
- \( \left( U_{1} \bigoplus U_{2} \right) + \left( W_{1} \bigoplus W_{2} \right) = \left( U_{1} + W_{1} \right) \bigoplus \left( U_{2} + W_{2} \right) \)
Does the following relation hold?
\[ \left( U_{1} \oplus U_{2} \right) \cap W = \left( U_{1} \cap W \right) \bigoplus \left( U_{2} \cap W \right) \]