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Given a Matroid (E,I), I is a set of independent subsets of E, right?

And independent subsets means that no two of these subsets must have an element in common, right?

Now according to the hereditary property of Matroids, if A is a subset of B which is a subset of E and if B belongs to I, then A also belongs to I.

If A is a subset of B, then all the elements in A are in B, then how are these two independent? All the sets that are supposed to belong to I (i.e. A and B in this case) must be independent (i.e. must not have any common element) right?

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