Question: 2. Let L be a regular language with = {0,1}. Define REMOVE(L) to be the language containing all strings that can be obtained by removing

2. Let L be a regular language with = {0,1}. Define

2. Let L be a regular language with = {0,1}. Define REMOVE(L) to be the language containing all strings that can be obtained by removing one symbol from the end of a string in L. So, REMOV E(L) = {2|TY E L where x S* and y S}. Show that the class of regular languages is closed under the REMOVE operation, i.e., given that L is regular then the language K = REMOVE(L) is also regular. Give both an intuitive proof by picture and a formal proof by construction as in Theorem 1.47 of Sipser

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