Anybody have idea about this problem?
let E be a finite set, C={S1,.....,Sm} a collection of subsets of E,
and let T = {e1,.....,et} subset of E. We say T is a traversal of C if
there exists distinct integers j(1),....j(t) such that ei belongs to
Sj(i),i=1,....,t. Let x be the set of all traversals of E. Show that
Mc=(E,x) is a matroid. What are the circuits, spans, and rank function
of Mc?
(Note: let M=(E,x) be a matroid and A subset of E. The rank of A in M,
r(A), is the cardinality of a maximal independent subset of A. A subset
D of E not in x is called dependent. A minimal dependent subset C of E
is called a circuit. A span of A ia a maximal superset S of A
satisfying r(S) = r(A))
please help me with correct approach....
thanx much
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