Question: a let s a b c d e and...

a) Let S = {a, b, c, d, e} and U = {{b, c, d}, {a, b}}. Expand the set U such that M = (S, U) is a matroid. Only add elements that are absolutely necessary. Justify their additions.
b) Show that the intersection of two matroids is not necessarily also a matroid. To do this, specify two matroids M1 = (S, U1) and M2 = (S, U2), for which the intersection M = (S, U1∩U2) is not a matroid.