(a) Show that there are, up to isomorphism, exactly 8 matroids
whose underlying set has three elements. Calling the elements
a,b,c, exhibit, for each of these matroids, its bases, cycles and
independent sets.
(b) Consider the matroid M on the set E = {a,b,c,d}, where the
bases are the subsets of E having precisely two elements. Detrmine
all the cycles of M, and show that there is no graph G such that M
is the cycle matroid M(G).