Product Recommendations: The action or practice of selling additional products or ser-vices to existing customers is called cross-selling. Giving product recommendation is one ofthe examples of cross-selling that are frequently used by online retailers. One simple methodto give product recommendations is to recommend products that are frequently browsed together by the customers. Suppose we want to recommend new products to the customer based on the products theyhave already browsed on the online website. Write a program using the A-priori algorithmto find products which are frequently browsed together. Fix the support to s

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.

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What is the name of the option in most presentation applications with which you can modify slide elements? 1. the option enables you to modify a slide element in most presentation applications.