1.43 Let A be any language. Define DROP-OUTOA) to be the language containing all strings that can be obtained by removing one symbol from a string in A. Thus DROP-OUT (A) tzzl ryz E A where r, z E y,y E St. Show that the class of regular languages is closed under the DROP-OUT operation. Give both a proof by picture and a more formal proof by construction as in Theorem 1.47 1.43 Let A be any language. Define DROP-OUTOA) to be the language containing all strings that can be obtained by removing one symbol from a string in A. Thus DROP-OUT (A) tzzl ryz E A where r, z E y,y E St. Show that the class of regular languages is closed under the DROP-OUT operation. Give both a proof by picture and a more formal proof by construction as in Theorem 1.47