Problem 1 (35 points): Let L be a regular language over some alphabet . Prove that the following language is also regular: For example, if the language L over = {0, 1.2} contains 0121 then Lstrange contains 1012. Optional hint: Since L is a regular language, there is a DFA M for L. Using M, think about constructing a new DFA Munge for Lsrangs by processing input symbols in pairs