"Explain why the arbitrary amounts of M1, M2, M3, M4 must always apply to (M1 U M3) \ (M2 U M4) C (M1 \ M2) U (M3 \ M4) "
Notice that $\displaystyle x \notin \left( {M_2 \cup M_4 } \right)\;\Rightarrow \quad x \notin {\rm M}_2 \wedge x \notin {\rm M}_4 $
Also $\displaystyle x \in M_1 \wedge x \notin M_2 \wedge x \notin M_4 \Rightarrow \quad x \in \left( {M_1 \backslash M_2 } \right)$