Identify at least three types of characteristics that you were asked about as you the computer identify a fruit.

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.

Which of the following is true of operations within a spreadsheet program’s built-in functions? a. operations within parentheses, then multiplication and division, and then addition and subtraction are computed. b. operations within parentheses, then addition and subtraction, and then multiplication and division are computed. c. multiplication and division, then addition and subtraction, and then operations within parentheses are computed. d. addition and subtraction, then multiplication and division, and then operations within parentheses are computed

Budgets you to do all of the following expect a) send frivolously b) avoid over spending c) gain financial independence d) examine your priorities and goals