Question: P 6. (20 points) Let S be a finite set, F a nonempty family of subsets of S that satisfies the hereditary axiom. Show that

P 6. (20 points) Let S be a finite set, F

P 6. (20 points) Let S be a finite set, F a nonempty family of subsets of S that satisfies the hereditary axiom. Show that if (S, F) is not a matroid, that is, does not satisfy the exchange axiom, then there exists a weight function w: S Ro such that Greedy((S,F), s) does not return a maximum weight basis of F, (a basis is a set in F that is not contained in any larger set in F) Hint: Consider two subsets A and B such that Al

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