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(20 marks) Give DFA's accepting the following languages over the alphabet S = {0, 2, 3, 5, 7): (a) the set of all strings beginning with a 7, 3 or 5, that, when the string is interpreted as an integer in base 9, is a multiple of 5 plus 2. For example: strings 7, 30, 35, 52, 502, 5002, 5057, 50057, 705, and 77777 are in the language; the strings 20, 00,022, 0020, 37 , 23, 33, 223, 2325, 2375, 3, 5, 33333,, 22222, 505, 22, 72, and 035 are not. (20 marks) Give DFA's accepting the following languages over the alphabet S = {0, 2, 3, 5, 7): (a) the set of all strings beginning with a 7, 3 or 5, that, when the string is interpreted as an integer in base 9, is a multiple of 5 plus 2. For example: strings 7, 30, 35, 52, 502, 5002, 5057, 50057, 705, and 77777 are in the language; the strings 20, 00,022, 0020, 37 , 23, 33, 223, 2325, 2375, 3, 5, 33333,, 22222, 505, 22, 72, and 035 are not