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Show that there is a language a ⚆ {0, 1} â— with the following properties: 1. for all x â a, |x| ≤ 5. 2. no dfa with fewer than 9 states recognizes a. hint: you don’t have to define a explicitly; just show that it has to exist. count the number of languages satisfying (1) and the number of dfas satisfying (2), and argue that there aren’t enough dfas to recognize all those languages. to count the number of languages satisfying (1), think about writing down all the strings of length at most 5, and then to define such a language, you have to make a binary decision for each string about whether to include it in the language or not. how many ways are there to make these choices? to count the number of dfas satisfying (2), consider that a dfa behaves identically even if you rename all the states, so you can assume without loss of generality that any dfa with k states has the state set {q1, q2, . . , qk}. now think about how to count how many ways there are to choose the other four parts of the dfa.

What best describes a career pathway in a lodging career? a worker starts out as an amusement attendant, then becomes a recreation worker, and then becomes a gaming worker within five years. a worker starts out as a bell hop, then becomes a night clerk, and then becomes a hotel manager within five years. a worker starting out as a tour guide, then becomes a travel clerk, and then becomes a travel agent within five years. a worker starts out as a server, then becomes a food preparer, and then becomes a head chef within five years.

If an improvement creates no significant change in a product’s performance, then it is a(n) ? a0 design improvement. (there are no answer choices)