Question: Show that if (S, I) is a matroid, then (S, I) is a matroid, where I = {A . S A contains some maximal

Show that if (S, I) is a matroid, then (S, I′) is a matroid, where I′ = {A′ . S − A′ contains some maximal A ∈ I} .

That is, the maximal independent sets of (S, I′) are just the complements of the maximal independent sets of (S, I).

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