8. Let k n, s = {1, 2, . . . , k}, and a = p (s) \ {}. In other words, the set a comprises all non-empty subsets of {1, 2, . . . , k}. For each a a, denote by min(a) the smallest element of a (notice that here a is a set). define a relation on a as follows: ab if and only if min(a) = min(b). Prove that is an equivalence relation on a. how many equivalence classes are there for a with respect to the relation ? define a relation on a as follows: ab if and only if either a = b or min(a) < min(b). Is a partial order on a? Is a total order on a?
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Answer: I think 45 is the answer
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