You are part of the team assigned to implement new software at XYZ Inc. The employees at XYZ Inc. trust the results obtained from the old software, but are cautious about accepting those from the proposed new software. What software implementation strategy would you recommend in this situation to allow users fall-back access to the old system as the new one is implemented

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.

Assume that there is a 4% rate of disk drive failure in a year. a. if all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. if copies of all your computer data are stored on three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

4. a1. vince owns a television repair shop that is insured undera commercial package policy. the policy includes thebuilding and personal property coverage form and thecauses-of-loss broad form. the declarations page indicatesthat coverage applies to both the building and the namedinsured's business property. explain whether or not thefollowing losses would be covered under his policy.a. a fire occurs on the premises, and the building isbadly damaged.b. a burglar steals some money and securities from anunlocked safe.c. a business computer is damaged by vandals whobreak into the shop after business hours.d. a tornado touches down near the store. several tel-evision sets of customers in the shop for repair aredamaged in the storm.til