(b) For a language L, define DROPOUT(L) to be the language containing all strings that can be obtained by removing one symbol from a string in L. Thus, DROPOUT(L) {ac : abc L,a,c {0,1}*, b {0,1}}. Show that the class of regular languages is closed under DROPOUT. That is if L is regular, then so is DROPOUT(L). [1 point] (Hint: Try to desgin a NFA for DROPOUT(L). To do so try to guess 'where the drop occurs, and use the idea from part(a). One idea is have two copies of the DFA for L, and then connect them based on a 'guess' for where the drop is. So for example, think about how you would recognize a string obtained from L by dropping the second symbol. ] (b) For a language L, define DROPOUT(L) to be the language containing all strings that can be obtained by removing one symbol from a string in L. Thus, DROPOUT(L) {ac : abc L,a,c {0,1}*, b {0,1}}. Show that the class of regular languages is closed under DROPOUT. That is if L is regular, then so is DROPOUT(L). [1 point] (Hint: Try to desgin a NFA for DROPOUT(L). To do so try to guess 'where the drop occurs, and use the idea from part(a). One idea is have two copies of the DFA for L, and then connect them based on a 'guess' for where the drop is. So for example, think about how you would recognize a string obtained from L by dropping the second symbol. ]