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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.

Aisha has finished working on a word processing document that contains 15 pages. she has added some special elements in the first three pages, page 9 and 10, and page 15 from the document. she wants to print only these pages to see how they look. which option is the correct way to represent (in the print dialog box) the pages that aisha wants to print

Description: write function lastfirst() that takes one argument—a list of strings of the format "lastname, firstname" —and returns a list consisting of two lists: (a) a list of all the last names (b) a list of all the first names