Problem 1 [10 points] Part (a) [5 points] Define the operation over languages L1, L2 as: L1 L2 = {w|(w e L1) 3 (w e L2)}. Show that regular languages are closed under D. That is, if L1 and L2 are regular, then L1 L2 is also regular. Part (b) [5 points] Define the CUT operation over languages L1, L2 as: LICUTL2 = {w |If w e L1 then w e L2, otherwise w & L2}. Show that regular languages are closed under CUT. That is, if L and L2 are regular, then LCUTL2 is also regular