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9 [10 pts A sequence over a set A (known as alphabet) is an infinite list of elements of A,a-(ao. a1, a2, ). The sequence a is periodic if there exists an integer T>0 so that ai aitT, for all 0, 1, 2 Such a T is called a period of the sequence a and the least such T is called the period, or sometimes the least period, of a. The sequence a is eventually periodic if there exist N >0 and T > 0 so that Equation (1) holds for all i2 N. A period (resp. the least period) of an eventually periodic sequence refers to a period (resp. least period) of the periodic part of a. Consider the following 1. In the alphabet (0,1), which of the following sequences is periodic (and what is the period) and which one is not? (0101)(0101)(0101) (01) (011) (0) 2. Prove that if a is a periodic (or eventually periodic) sequence with least period T then every period of a is a multiple of T