is used to create a document for multiple recipients.​

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.

Following are uses of spreadsheets. for each use, choose whether the use is a business use, consumer use, or student use. family budget: sales data: recording research data for science class:

Dereck works for long hours on his computer.  he frequently experiences physical strain by the end of the day because he does not follow an important rule of ergonomics with respect to the use of keyboards.  which of the following actions of dereck could lead to physical strain? a.  placing the keyboard exactly in front of him while typingb.  keeping hands and wrists straight while typingc.  using wrist pads throughout the dayd.  pounding at the keys on the keyboard while typinge.  resting his hands on the keyboard when he is not typing