Let Em : {partitions 71 of [n] : {1, ., n}} Where a partition is an unordered set of subsets 7T = Sll - - - IS;C = {$1, .,Sk} With Sl- C [n] such...

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1. LetEm : {partitions 71 of [n] : {1, ..., n}} Where a partition is an unordered set of subsets7T = Sll - - - IS;C = {$1, ...,Sk} With Sl- C [n] such that each element of [n] is in exactly one of the Si. Find a formulafor ”(0, 1) for n = 4, Where u is the Mobius function of this partially ordered set7Where 0:1|---|'n,, 121...”are the smallest and largest elements, respectively. 2. Prove a formula for the Mobius function of the partially ordered setZ20 X Z20 Where((1,1)) g (ad) ifa g C, and bg d