Is 583 a string or a number?

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.

The head restraint should be adjusted so that it reaches a.the top of your ears b.the base of your skull c.the top of the head

Allison and her group have completed the data entry for their spreadsheet project. they are in the process of formatting the data to make it easier to read and understand. the title is located in cell a5. the group has decided to merge cells a3: a7 to attempt to center the title over the data. after the merge, allison points out that it is not centered and looks bad. where would the title appear if allison unmerged the cells in an attempt to fix the title problem?