# Question: Show that if S is a matroid then S

Show that if (S, ℓ) is a matroid, then (S, ℓ′) is a matroid, where
ℓ′ = {A′: S - A′ contains some maximal A ¬ℓ}.

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

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

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