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4. Given is a set A. In each of the following case design a first order lantuage, once using only function symbols and once using

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4. Given is a set A. In each of the following case design a first order lantuage, once using only function symbols and once using only relation symbols such that the given mathematical structure can be viewed as an L-structure. As in Problem 3, do not forget to specify np to each function symbol F and nr to each relation symbol R. (a) The domain of the structure is N+. The function/relation is the assighment (a,b) = the smallest common multiple of a b (b) The domain of the structure is Pain(N+) = the set of all finite subsets of N+ The function/relation is the assighment X the set of all divisors of numbers in X

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