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max no of subsets, having none is a subset of another

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April 23, 2009

Problem Statement

What is the maximum number of subsets, having property that none of them is a subset of another, can a set with 10 elements have?
<spanclass=′latex−bold′>(A)</span> 126<spanclass=′latex−bold′>(B)</span> 210<spanclass=′latex−bold′>(C)</span> 252<spanclass=′latex−bold′>(D)</span> 420<spanclass=′latex−bold′>(E)</span> 1024<span class='latex-bold'>(A)</span>\ 126 \qquad<span class='latex-bold'>(B)</span>\ 210 \qquad<span class='latex-bold'>(C)</span>\ 252 \qquad<span class='latex-bold'>(D)</span>\ 420 \qquad<span class='latex-bold'>(E)</span>\ 1024
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