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Question: in the united states any licensed prescriber of controlled substances...

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In the United States, any licensed prescriber of controlled substances is issued a DEA number in the format stxxxxxxx, where s denotes one of the seven letters in the set {A, B, F, G, M, P, R t can be any of the 26 letters of the alphabet, or the digit 9. . x is any digit. Assume that any string in this form is a valid DEA number.1 Let P(n) be the statement The first character of DEA number n is a consonant, and Q(n) be the statement The last digit of DEA number n is even. (a) Compute the number of DEA numbers which make each of the following statements true: (b) Which is easier to compute: the number of DEA numbers which make P(n)AQ(n) true, or the number of DEA numbers which make P(n) VQ( true? Explain why. (c) Based on your answer to part (b) and your knowledge of DeMorgans Law, compute efficiently the number of DEA numbers which make each of the following statements true:

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