1: Closure Properties of Regular Languages (a) (5pts) Give an FA (DFA or NFA) for the following language over alphabet S = {x,y). Note the FA can be constructed by combining DFAs for simpler languages. Ls = {w has odd length or an even number of r 's } (b) (5pts)Give an FA for the following language over alphabet S = {r,y). Note the FA can be constructed by combining DFAs for simpler languages. L6 = {| has odd length and an even number of r 's } Impair (c) (5pts) If L is a language over alphabet 2 = {0,1} then we define Imp(L) as: Imp(L) = {W E L w has odd length} Let L1 = {4,0,1,00, 111, 1001,00000}, what is Imp(Li)? Show that the class of regular languages is closed under Imp (i.e. you need to show that for any regular language L, Imp(L) is regular as well) (d) (5pts) If L is a language then we define DELI(L) as: DELI(L) = {wl if w can be obtained by deleting one symbol of a string in L} Let L1 = {4,1,00, 101), what is DELI(L1)? Show that the class of regular languages is closed under DELI (i.e. you need to show that for any regular language L, DELI(L) is regular as well)