Let = {0, 1, 2} be an alphabet.

(a) Write out some strings contained in the set

(b) Let L be the language defined by the set of all strings from that do not contain a 1 (i.e. only strings with zero or two are allowed). Write out some strings contained in this language.

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(c) Instead of using 0, 2 as the symbols for L, use a, b and write out some strings contained in this language.

(d) Now consider/interpret as the set of all possible real numbers contained on the interval [0, 1] represented in base 3. Should we interpret L as the set of all possible real numbers contained on the interval [0, 1] represented in base 2 (i.e. the set of all possible binary numbers contained in [0, 1])?

7. Let = {0, 1} be an alphabet. Now consider/interpret as the set of all possible real numbers R contained on the interval [0, 1] represented in base 2. Let L be the language defined by the set of strings contained in Q (the set of rational numbers). Given a string in , describe an algorithm that will determine if L (i.e. describe an procedure to either accept or reject ).