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