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Question 1: Regular Languages (6 Marks) Argue that each of the following languages is regular by showing how to construct it using the definition of regular languages: a. (2 marks) The language of all binary strings of even length. b. (2 marks) The language of strings over the alphabet {a,b,c} in which every a is followed by a c. So the string acbbbacccbacbccb is in the language because every a is followed by a c. The strings abcacccbc and cbbcaaccacob are not in the language because of the highlighted occurrences of a that are not followed by a c. C. (2 marks) The language of all binary strings with an odd number of Os or a number of 1s that is divisible by 3. The strings 011001110110, 011001101001, and 0110011010010 belong to the language: 011001110110 contains an odd number of os, 011001101001 contains a number of 1s divisible by 3, and 0110011010010 satisfies both conditions. The string 01101001100 is not in the language because it contains an even number of Os and the number of 1s is not divisible by 3. highlighted occurrences of a that are not followed by a c. a