Let be an alphabet. For any languages A, B, C , define the majority of A, B, and C as the language Maj(A,B,C)={ x | x is contained in at least two of A, B, or C }. Prove that the DFA-recognizable languages are closed under majority, i.e., if A, B, and C are DFA-recognizable, then Maj(A, B, C) is DFA-recognizable. Your proof should be a direct construction of a DFA recognizing Maj(A,B,C), similar to the DFA product construction covered in lecture. In other words, fully define a DFA recognizing Maj(A,B,C), which works by simulating DFAs for A, B, and C as in the product construction, rather than simply proving that it exists via closure properties of regular languages.