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(a) Show that there are, up to isomorphism, exactly 8 matroids whose underlying set has three...

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Advance Math

(a) Show that there are, up to isomorphism, exactly 8 matroidswhose underlying set has three elements. Calling the elementsa,b,c, exhibit, for each of these matroids, its bases, cycles andindependent sets.

(b) Consider the matroid M on the set E = {a,b,c,d}, where thebases are the subsets of E having precisely two elements. Detrmineall the cycles of M, and show that there is no graph G such that Mis the cycle matroid M(G).

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