Explore BrainMass

Linearly Independent Subsets : Partially Ordered by Inclusion

Let X be any vector space over the field F, let L be a linearly independent subset
of X, and A be the set of linearly independent subsets of X containing L.
Then A is partially ordered by inclusion - why does it follow?

Solution Preview

Because inclusion is a partial order on ANY family of subsets.
You just have to check A subset A for all A, A ...

Solution Summary

Partially Ordered by Inclusion is investigated.