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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.

The word ‘play’ comes with many different interpretations and a variety of definitions. discuss some of the various meanings tied to the word play. why is the concept of play thought to be an important addition to the workplace? do some (brief) research online and give an example of how play in the workplace is being done right.

What is one way in which tablets differ from laptops and notebooks? tablets are designed for touch-based interaction. tablets are designed to be used as desktops. tablets are designed for input via a keyboard and mouse. tablets are designed to be larger than laptops.