Assume L1 is regular, and L2, L3 are context-free. For each of the following parts, use language closure properties to prove the statement or provide a counter-example to disprove the statement:

(a) (L1 L2) L3 is context-free. (b) (L1 L2) L3 is context-free.

(c) (L1 L2) (L1 \ L3) is context-free. (d) (L2 L3) L1 is regular.

(e) (L2 \ L3) L1 is not context-free.