Question: Please answer the following: [8 4. Consider a DTMC {Xn, n E N} on a state space denoted by S. Let B be a set

Please answer the following:

[8 4. Consider a DTMC {Xn, n E N} on a state space denoted by S. Let B be a set of states such that B C S. Does the statement P(Xn+1 = Enti| Xn E B, Xn-1 = En-1, . . ., Xo = X0) = P(Xn+1 = UntilXn E B) always hold true? If yes, prove this statement. If no, provide a counterexample

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