3. (20 marks) Give DFA's accepting the following languages over the alphabet = {0,1,3,4,6}: (a) the set of all strings beginning with a 1, 3 or 6, that, when the string is interpreted as an integer in base 7, is a multiple of 4 plus 1. For example: . strings 1, 16, 111, 166, 331, 643, 3646, 3334, 36411 and 36433 are in the language: the strings 10, 00,011, 0010, 36, 13, 23, 113, 1313, 2347,2, 21, 161, 3333, 606, 44, 41, and 041 are not. (b) The set of all strings that ends with an 1, 3, or 6 and when the string is interpreted in reverse as an integer in base 7, is a multiple of 4 plus 1. Examples of strings in the language are 1, 61, 111, 661, 133, 346, 6463, 4333, 11463 and 33463 Examples of strings that are not in the language are: 01, 00,110, 0100, 63 , 31, 32, 311, 3131, 7432, 2, 12, 161, 3333, 606, 44, 14, and 140. 3. (20 marks) Give DFA's accepting the following languages over the alphabet = {0,1,3,4,6}: (a) the set of all strings beginning with a 1, 3 or 6, that, when the string is interpreted as an integer in base 7, is a multiple of 4 plus 1. For example: . strings 1, 16, 111, 166, 331, 643, 3646, 3334, 36411 and 36433 are in the language: the strings 10, 00,011, 0010, 36, 13, 23, 113, 1313, 2347,2, 21, 161, 3333, 606, 44, 41, and 041 are not. (b) The set of all strings that ends with an 1, 3, or 6 and when the string is interpreted in reverse as an integer in base 7, is a multiple of 4 plus 1. Examples of strings in the language are 1, 61, 111, 661, 133, 346, 6463, 4333, 11463 and 33463 Examples of strings that are not in the language are: 01, 00,110, 0100, 63 , 31, 32, 311, 3131, 7432, 2, 12, 161, 3333, 606, 44, 14, and 140