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n set with 4 elements

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April 28, 2009
algorithmabstract algebragroup theory

Problem Statement

There are n n sets having 4 4 elements each. The difference set of any two of the sets is equal to one of the n n sets. n n can be at most ? (A difference set of AA and BB is (A∖B)∪(B∖A) (A\setminus B)\cup(B\setminus A) )
<spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 7<spanclass=′latex−bold′>(D)</span> 15<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ 3 \qquad<span class='latex-bold'>(B)</span>\ 5 \qquad<span class='latex-bold'>(C)</span>\ 7 \qquad<span class='latex-bold'>(D)</span>\ 15 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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